diff -rupN --no-dereference Python-3.10.9/Lib/distutils/command/build_ext.py Python-3.10.9-new/Lib/distutils/command/build_ext.py
--- Python-3.10.9/Lib/distutils/command/build_ext.py	2022-12-06 19:31:21.000000000 +0100
+++ Python-3.10.9-new/Lib/distutils/command/build_ext.py	2022-12-08 09:36:57.667024823 +0100
@@ -218,12 +218,13 @@ class build_ext(Command):
 
         # For extensions under Cygwin, Python's library directory must be
         # appended to library_dirs
-        if sys.platform[:6] == 'cygwin':
+        if sys.platform[:6] == 'cygwin' or self.plat_name.startswith(('mingw')):
             if sys.executable.startswith(os.path.join(sys.exec_prefix, "bin")):
                 # building third party extensions
+                config_dir_name = os.path.basename(sysconfig.get_config_var('LIBPL'))
                 self.library_dirs.append(os.path.join(sys.prefix, "lib",
                                                       "python" + get_python_version(),
-                                                      "config"))
+                                                      config_dir_name))
             else:
                 # building python standard extensions
                 self.library_dirs.append('.')
diff -rupN --no-dereference Python-3.10.9/Lib/distutils/command/install.py Python-3.10.9-new/Lib/distutils/command/install.py
--- Python-3.10.9/Lib/distutils/command/install.py	2022-12-06 19:31:21.000000000 +0100
+++ Python-3.10.9-new/Lib/distutils/command/install.py	2022-12-08 09:36:57.667024823 +0100
@@ -72,8 +72,8 @@ if HAS_USER_SITE:
     INSTALL_SCHEMES['nt_user'] = {
         'purelib': '$usersite',
         'platlib': '$usersite',
-        'headers': '$userbase/Python$py_version_nodot/Include/$dist_name',
-        'scripts': '$userbase/Python$py_version_nodot/Scripts',
+        'headers': '$userbase/include/python$py_version_short$abiflags/$dist_name',
+        'scripts': '$userbase/bin',
         'data'   : '$userbase',
         }
 
diff -rupN --no-dereference Python-3.10.9/Lib/sysconfig.py Python-3.10.9-new/Lib/sysconfig.py
--- Python-3.10.9/Lib/sysconfig.py	2022-12-06 19:31:21.000000000 +0100
+++ Python-3.10.9-new/Lib/sysconfig.py	2022-12-08 09:36:57.668024823 +0100
@@ -47,13 +47,13 @@ _INSTALL_SCHEMES = {
         'data': '{base}',
         },
     'nt': {
-        'stdlib': '{installed_base}/Lib',
-        'platstdlib': '{base}/Lib',
-        'purelib': '{base}/Lib/site-packages',
-        'platlib': '{base}/Lib/site-packages',
-        'include': '{installed_base}/Include',
-        'platinclude': '{installed_base}/Include',
-        'scripts': '{base}/Scripts',
+        'stdlib': '{installed_base}/lib/python{py_version_short}',
+        'platstdlib': '{base}/lib/python{py_version_short}',
+        'purelib': '{base}/lib/python{py_version_short}/site-packages',
+        'platlib': '{base}/lib/python{py_version_short}/site-packages',
+        'include': '{installed_base}/include/python{py_version_short}',
+        'platinclude': '{installed_base}/include/python{py_version_short}',
+        'scripts': '{base}/bin',
         'data': '{base}',
         },
     }
@@ -89,12 +89,12 @@ if _HAS_USER_BASE:
     _INSTALL_SCHEMES |= {
         # NOTE: When modifying "purelib" scheme, update site._get_path() too.
         'nt_user': {
-            'stdlib': '{userbase}/Python{py_version_nodot_plat}',
-            'platstdlib': '{userbase}/Python{py_version_nodot_plat}',
-            'purelib': '{userbase}/Python{py_version_nodot_plat}/site-packages',
-            'platlib': '{userbase}/Python{py_version_nodot_plat}/site-packages',
-            'include': '{userbase}/Python{py_version_nodot_plat}/Include',
-            'scripts': '{userbase}/Python{py_version_nodot_plat}/Scripts',
+            'stdlib': '{userbase}/lib/python{py_version_short}',
+            'platstdlib': '{userbase}/lib/python{py_version_short}',
+            'purelib': '{userbase}/lib/python{py_version_short}/site-packages',
+            'platlib': '{userbase}/lib/python{py_version_short}/site-packages',
+            'include': '{userbase}/include/python{py_version_short}',
+            'scripts': '{userbase}/bin',
             'data': '{userbase}',
             },
         'posix_user': {
@@ -487,7 +487,7 @@ def _init_non_posix(vars):
     vars['INCLUDEPY'] = get_path('include')
     vars['EXT_SUFFIX'] = _imp.extension_suffixes()[0]
     vars['EXE'] = '.exe'
-    vars['VERSION'] = _PY_VERSION_SHORT_NO_DOT
+    vars['VERSION'] = _PY_VERSION_SHORT
     vars['BINDIR'] = os.path.dirname(_safe_realpath(sys.executable))
     vars['TZPATH'] = ''