diff --git a/Lib/test/test_imp.py b/Lib/test/test_imp.py
index 7269f5aee2e4afc..e81eb6f0a86fe86 100644
--- a/Lib/test/test_imp.py
+++ b/Lib/test/test_imp.py
@@ -294,6 +294,12 @@ def clean_up():
             if lookedup is not _testsinglephase:
                 raise Exception((_testsinglephase, lookedup))
 
+            # Attrs set in the module init func are in m_copy.
+            _initialized = _testsinglephase._initialized
+            initialized = _testsinglephase.initialized()
+            if _initialized != initialized:
+                raise Exception((_initialized, initialized))
+
             # Attrs set after loading are not in m_copy.
             if hasattr(_testsinglephase, 'spam'):
                 raise Exception(_testsinglephase.spam)
diff --git a/Modules/_testsinglephase.c b/Modules/_testsinglephase.c
index 8d72cc08451a1f0..565221c887e5aef 100644
--- a/Modules/_testsinglephase.c
+++ b/Modules/_testsinglephase.c
@@ -134,6 +134,16 @@ init_module(PyObject *module, module_state *state)
     if (PyModule_AddObjectRef(module, "str_const", state->str_const) != 0) {
         return -1;
     }
+
+    double d = _PyTime_AsSecondsDouble(state->initialized);
+    PyObject *initialized = PyFloat_FromDouble(d);
+    if (initialized == NULL) {
+        return -1;
+    }
+    if (PyModule_AddObjectRef(module, "_initialized", initialized) != 0) {
+        return -1;
+    }
+
     return 0;
 }