diff --git a/gcc/cp/decl.cc b/gcc/cp/decl.cc
index 070f673c3a2..80467c19254 100644
--- a/gcc/cp/decl.cc
+++ b/gcc/cp/decl.cc
@@ -8180,6 +8180,12 @@ cp_finish_decl (tree decl, tree init, bool init_const_expr_p,
 	  return;
 	}
       cp_apply_type_quals_to_decl (cp_type_quals (type), decl);
+
+      /* Update the type of the corresponding TEMPLATE_DECL to match.  */
+      if (DECL_LANG_SPECIFIC (decl)
+	  && DECL_TEMPLATE_INFO (decl)
+	  && DECL_TEMPLATE_RESULT (DECL_TI_TEMPLATE (decl)) == decl)
+	TREE_TYPE (DECL_TI_TEMPLATE (decl)) = type;
     }
 
   if (ensure_literal_type_for_constexpr_object (decl) == error_mark_node)
diff --git a/gcc/testsuite/g++.dg/modules/auto-3.h b/gcc/testsuite/g++.dg/modules/auto-3.h
new file mode 100644
index 00000000000..f129433cbcb
--- /dev/null
+++ b/gcc/testsuite/g++.dg/modules/auto-3.h
@@ -0,0 +1,10 @@
+template<class>
+struct __tree_barrier {
+  static const auto __phase_alignment_1 = 0;
+
+  template<class>
+  static const auto __phase_alignment_2 = 0;
+};
+
+template<class>
+inline auto __phase_alignment_3 = 0;
diff --git a/gcc/testsuite/g++.dg/modules/auto-3_a.H b/gcc/testsuite/g++.dg/modules/auto-3_a.H
new file mode 100644
index 00000000000..25a7a73e73e
--- /dev/null
+++ b/gcc/testsuite/g++.dg/modules/auto-3_a.H
@@ -0,0 +1,4 @@
+// { dg-additional-options "-fmodule-header" }
+// { dg-module-cmi {} }
+
+#include "auto-3.h"
diff --git a/gcc/testsuite/g++.dg/modules/auto-3_b.C b/gcc/testsuite/g++.dg/modules/auto-3_b.C
new file mode 100644
index 00000000000..03b6d46f476
--- /dev/null
+++ b/gcc/testsuite/g++.dg/modules/auto-3_b.C
@@ -0,0 +1,4 @@
+// { dg-additional-options "-fmodules-ts -fno-module-lazy" }
+
+#include "auto-3.h"
+import "auto-3_a.H";