diff --git a/pytypes/typechecker.py b/pytypes/typechecker.py
index a0cd92b..b6b4342 100644
--- a/pytypes/typechecker.py
+++ b/pytypes/typechecker.py
@@ -964,15 +964,19 @@ def typechecked_module(md, force_recursive = False):
     """
     if not pytypes.checking_enabled:
         return md
+    # Save input to return original string if input was a string.
+    md_arg = md
     if isinstance(md, str):
         if md in sys.modules:
             md = sys.modules[md]
             if md is None:
-                return md
+                return md_arg
         elif md in _pending_modules:
             # if import is pending, we just store this call for later
             _pending_modules[md].append(lambda t: typechecked_module(t, True))
-            return md
+            return md_arg
+        else:
+            raise KeyError('Found no module {!r} to typecheck'.format(md))
     assert(ismodule(md))
     if md.__name__ in _pending_modules:
             # if import is pending, we just store this call for later
@@ -981,7 +985,7 @@ def typechecked_module(md, force_recursive = False):
             # todo: Issue warning here that not the whole module might be covered yet
     if md.__name__ in _fully_typechecked_modules and \
             _fully_typechecked_modules[md.__name__] == len(md.__dict__):
-        return md
+        return md_arg
     # To play it safe we avoid to modify the dict while iterating over it,
     # so we previously cache keys.
     # For this we don't use keys() because of Python 3.
@@ -997,7 +1001,7 @@ def typechecked_module(md, force_recursive = False):
                 typechecked_class(memb, force_recursive, force_recursive)
     if not md.__name__ in _pending_modules:
         _fully_typechecked_modules[md.__name__] = len(md.__dict__)
-    return md
+    return md_arg
 
 
 def typechecked(memb):

diff --git a/tests/test_typechecker.py b/tests/test_typechecker.py
index fc4483d..60546b5 100644
--- a/tests/test_typechecker.py
+++ b/tests/test_typechecker.py
@@ -2651,8 +2651,14 @@ class TestTypecheck_module(unittest.TestCase):
     def test_function_py2(self):
         from testhelpers import modulewide_typecheck_testhelper_py2 as mth
         self.assertEqual(mth.testfunc(3, 2.5, 'abcd'), (9, 7.5))
+        with self.assertRaises(KeyError):
+            pytypes.typechecked_module('nonexistent123')
         self.assertEqual(mth.testfunc(3, 2.5, 7), (9, 7.5)) # would normally fail
-        pytypes.typechecked_module(mth)
+        module_name = 'testhelpers.modulewide_typecheck_testhelper_py2'
+        returned_mth = pytypes.typechecked_module(module_name)
+        self.assertEqual(returned_mth, module_name)
+        returned_mth = pytypes.typechecked_module(mth)
+        self.assertEqual(returned_mth, mth)
         self.assertEqual(mth.testfunc(3, 2.5, 'abcd'), (9, 7.5))
         self.assertRaises(InputTypeError, lambda: mth.testfunc(3, 2.5, 7))
 
@@ -2662,7 +2668,8 @@ class TestTypecheck_module(unittest.TestCase):
         from testhelpers import modulewide_typecheck_testhelper as mth
         self.assertEqual(mth.testfunc(3, 2.5, 'abcd'), (9, 7.5))
         self.assertEqual(mth.testfunc(3, 2.5, 7), (9, 7.5)) # would normally fail
-        pytypes.typechecked_module(mth)
+        returned_mth = pytypes.typechecked_module(mth)
+        self.assertEqual(returned_mth, mth)
         self.assertEqual(mth.testfunc(3, 2.5, 'abcd'), (9, 7.5))
         self.assertRaises(InputTypeError, lambda: mth.testfunc(3, 2.5, 7))
 

typechecked(string) should have more consistent return type
Currently if you call `typechecked` on a string module name, it has case-by-case behavior to sometimes return the original string and sometimes return the resolved module:
```python
typechecked('requests') → <module 'requests'>
typechecked('requests') → 'requests'
```

Could we simplify to make it unconditionally return the value that was passed in, str→str, module→module, class→class, etc?
tests/test_typechecker.py::TestTypecheck_module::test_function_py2
tests/test_typechecker.py::testClass2_defTimeCheck tests/test_typechecker.py::testClass2_defTimeCheck2 tests/test_typechecker.py::testClass2_defTimeCheck3 tests/test_typechecker.py::testClass2_defTimeCheck4 tests/test_typechecker.py::testClass3_defTimeCheck tests/test_typechecker.py::testClass2_defTimeCheck_init_ov tests/test_typechecker.py::testfunc_check_argument_types_empty tests/test_typechecker.py::testfunc_varargs1 tests/test_typechecker.py::testfunc_varargs4 tests/test_typechecker.py::testfunc_varargs_ca1 tests/test_typechecker.py::testfunc_varargs_ca4 tests/test_typechecker.py::TestTypecheck::test_abstract_override tests/test_typechecker.py::TestTypecheck::test_annotations_from_typestring tests/test_typechecker.py::TestTypecheck::test_callable tests/test_typechecker.py::TestTypecheck::test_classmethod tests/test_typechecker.py::TestTypecheck::test_custom_annotations tests/test_typechecker.py::TestTypecheck::test_custom_generic tests/test_typechecker.py::TestTypecheck::test_defaults_inferred_types tests/test_typechecker.py::TestTypecheck::test_function tests/test_typechecker.py::TestTypecheck::test_get_types tests/test_typechecker.py::TestTypecheck::test_method tests/test_typechecker.py::TestTypecheck::test_method_forward tests/test_typechecker.py::TestTypecheck::test_parent_typecheck_no_override tests/test_typechecker.py::TestTypecheck::test_property tests/test_typechecker.py::TestTypecheck::test_staticmethod tests/test_typechecker.py::TestTypecheck::test_typecheck_parent_type tests/test_typechecker.py::TestTypecheck::test_typestring_varargs_syntax tests/test_typechecker.py::TestTypecheck::test_typevar_class tests/test_typechecker.py::TestTypecheck::test_typevar_collision tests/test_typechecker.py::TestTypecheck::test_various tests/test_typechecker.py::TestTypecheck_class::test_classmethod tests/test_typechecker.py::TestTypecheck_class::test_method tests/test_typechecker.py::TestTypecheck_class::test_staticmethod tests/test_typechecker.py::TestTypecheck_module::test_function_py3 tests/test_typechecker.py::Test_check_argument_types::test_function tests/test_typechecker.py::Test_check_argument_types::test_inner_class tests/test_typechecker.py::Test_check_argument_types::test_inner_method tests/test_typechecker.py::Test_check_argument_types::test_methods tests/test_typechecker.py::TestOverride::test_auto_override tests/test_typechecker.py::TestOverride::test_override tests/test_typechecker.py::TestOverride::test_override_at_definition_time tests/test_typechecker.py::TestOverride::test_override_at_definition_time_with_forward_decl tests/test_typechecker.py::TestOverride::test_override_diamond tests/test_typechecker.py::TestOverride::test_override_typecheck tests/test_typechecker.py::TestOverride::test_override_typecheck_class tests/test_typechecker.py::TestOverride::test_override_vararg tests/test_typechecker.py::TestStubfile::test_annotations_from_stubfile_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_annotations_from_stubfile_plain_3_5_stub tests/test_typechecker.py::TestStubfile::test_callable_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_custom_generic_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_defaults_inferred_types_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_defaults_inferred_types_plain_3_5_stub tests/test_typechecker.py::TestStubfile::test_override_diamond_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_override_diamond_plain_3_5_stub tests/test_typechecker.py::TestStubfile::test_property_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_property_plain_3_5_stub tests/test_typechecker.py::TestStubfile::test_typecheck_parent_type_plain_2_7_stub tests/test_typechecker.py::TestStubfile::test_typecheck_parent_type_plain_3_5_stub tests/test_typechecker.py::TestTypecheck_Python3_5::test_abstract_override_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_callable_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_classmethod_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_custom_generic_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_defaults_inferred_types tests/test_typechecker.py::TestTypecheck_Python3_5::test_defaults_with_missing_annotations_class tests/test_typechecker.py::TestTypecheck_Python3_5::test_defaults_with_missing_annotations_plain tests/test_typechecker.py::TestTypecheck_Python3_5::test_defaults_with_missing_annotations_property tests/test_typechecker.py::TestTypecheck_Python3_5::test_defaults_with_missing_annotations_static tests/test_typechecker.py::TestTypecheck_Python3_5::test_function_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_get_types_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_method_forward_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_method_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_parent_typecheck_no_override_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_property tests/test_typechecker.py::TestTypecheck_Python3_5::test_staticmethod_py3 tests/test_typechecker.py::TestTypecheck_Python3_5::test_typecheck_parent_type tests/test_typechecker.py::TestTypecheck_Python3_5::test_various_py3 tests/test_typechecker.py::TestOverride_Python3_5::test_auto_override tests/test_typechecker.py::TestOverride_Python3_5::test_override_at_definition_time tests/test_typechecker.py::TestOverride_Python3_5::test_override_at_definition_time_with_forward_decl tests/test_typechecker.py::TestOverride_Python3_5::test_override_diamond tests/test_typechecker.py::TestOverride_Python3_5::test_override_py3 tests/test_typechecker.py::TestOverride_Python3_5::test_override_typecheck tests/test_typechecker.py::TestOverride_Python3_5::test_override_vararg tests/test_typechecker.py::Test_check_argument_types_Python3_5::test_function tests/test_typechecker.py::Test_check_argument_types_Python3_5::test_inner_class tests/test_typechecker.py::Test_check_argument_types_Python3_5::test_inner_method tests/test_typechecker.py::Test_check_argument_types_Python3_5::test_methods tests/test_typechecker.py::Test_utils::test_Generator_is_of_type tests/test_typechecker.py::Test_utils::test_bound_typevars_readonly tests/test_typechecker.py::Test_utils::test_empty_values tests/test_typechecker.py::Test_utils::test_forward_declaration_infinite_recursion tests/test_typechecker.py::Test_utils::test_has_type_hints_on_slot_wrapper tests/test_typechecker.py::Test_utils::test_resolve_fw_decl tests/test_typechecker.py::Test_utils::test_tuple_ellipsis tests/test_typechecker.py::Test_utils::test_tuple_ellipsis_check tests/test_typechecker.py::Test_utils::test_type_bases tests/test_typechecker.py::Test_combine_argtype::test_exceptions tests/test_typechecker.py::Test_combine_argtype::test_function tests/test_typechecker.py::Test_agent::test_function_agent tests/test_typechecker.py::Test_agent::test_init_agent_return_None tests/test_typechecker.py::Test_agent::test_method_agent_return tests/test_typechecker.py::Test_agent_Python3_5::test_function_agent tests/test_typechecker.py::Test_agent_Python3_5::test_init_agent_return_None tests/test_typechecker.py::Test_agent_Python3_5::test_method_agent_return