diff --git a/src/lightning/fabric/utilities/cloud_io.py b/src/lightning/fabric/utilities/cloud_io.py
index fd3196202f8e2..dee220efb3f85 100644
--- a/src/lightning/fabric/utilities/cloud_io.py
+++ b/src/lightning/fabric/utilities/cloud_io.py
@@ -120,6 +120,7 @@ def _atomic_save(checkpoint: dict[str, Any], filepath: _PATH) -> None:
             raise RuntimeError(
                 'Upgrade fsspec to enable cross-device local checkpoints: pip install "fsspec[http]>=2025.5.0"',
             ) from e
+        raise
 
 
 def _is_object_storage(fs: AbstractFileSystem) -> bool:
diff --git a/tests/tests_fabric/utilities/test_cloud_io.py b/tests/tests_fabric/utilities/test_cloud_io.py
index 7e934e5dc86b4..d128240846d87 100644
--- a/tests/tests_fabric/utilities/test_cloud_io.py
+++ b/tests/tests_fabric/utilities/test_cloud_io.py
@@ -11,10 +11,12 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import errno
 import os
 from unittest import mock
 
 import fsspec
+import pytest
 import torch
 from fsspec.implementations.local import LocalFileSystem
 from fsspec.spec import AbstractFileSystem
@@ -150,3 +152,36 @@ def test_atomic_save_uses_write_for_local(tmp_path):
     assert filepath.exists()
     loaded = torch.load(filepath, weights_only=True)
     torch.testing.assert_close(loaded["key"], checkpoint["key"])
+
+
+def test_atomic_save_permission_error_propagation():
+    """Test that _atomic_save propagates PermissionError if it is not an EXDEV error."""
+    checkpoint = {"key": torch.tensor([1, 2, 3])}
+    filepath = "memory://checkpoint.ckpt"
+
+    mock_fs = mock.MagicMock()
+    mock_fs.open.side_effect = PermissionError("Permission denied")
+    mock_fs.pipe.side_effect = PermissionError("Permission denied")
+
+    with mock.patch("fsspec.core.url_to_fs", return_value=(mock_fs, "checkpoint.ckpt")):
+        with pytest.raises(PermissionError, match="Permission denied"):
+            _atomic_save(checkpoint, filepath)
+
+
+def test_atomic_save_exdev_to_runtime_error():
+    """Test that _atomic_save maps PermissionError with EXDEV context to RuntimeError."""
+    checkpoint = {"key": torch.tensor([1, 2, 3])}
+    filepath = "memory://checkpoint.ckpt"
+
+    mock_fs = mock.MagicMock()
+
+    os_error = OSError(errno.EXDEV, "Cross-device link")
+    permission_error = PermissionError("Permission denied")
+    permission_error.__context__ = os_error
+
+    mock_fs.open.side_effect = permission_error
+    mock_fs.pipe.side_effect = permission_error
+
+    with mock.patch("fsspec.core.url_to_fs", return_value=(mock_fs, "checkpoint.ckpt")):
+        with pytest.raises(RuntimeError, match="Upgrade fsspec to enable cross-device local checkpoints"):
+            _atomic_save(checkpoint, filepath)
diff --git a/tests/tests_pytorch/trainer/connectors/test_checkpoint_connector.py b/tests/tests_pytorch/trainer/connectors/test_checkpoint_connector.py
index 1450a92ed2744..59c76602d90bb 100644
--- a/tests/tests_pytorch/trainer/connectors/test_checkpoint_connector.py
+++ b/tests/tests_pytorch/trainer/connectors/test_checkpoint_connector.py
@@ -118,19 +118,23 @@ def test_local_cross_device_checkpoint(tmpdir):
     )
     trainer.fit(model)
     # Simulate the behavior of fsspec when writing to a local file system but other device.
-    with (
-        mock.patch("os.rename", side_effect=OSError(errno.EXDEV, "Invalid cross-device link")),
-        mock.patch("os.chmod", side_effect=PermissionError("Operation not permitted")),
-    ):
-        if compare_version("fsspec", operator.lt, "2025.5.0"):
-            with pytest.raises(
+    if compare_version("fsspec", operator.lt, "2025.5.0"):
+        with (
+            mock.patch("os.rename", side_effect=OSError(errno.EXDEV, "Invalid cross-device link")),
+            mock.patch("os.chmod", side_effect=PermissionError("Operation not permitted")),
+            pytest.raises(
                 RuntimeError,
                 match=re.escape(
                     'Upgrade fsspec to enable cross-device local checkpoints: pip install "fsspec[http]>=2025.5.0"'
                 ),
-            ):
-                trainer.save_checkpoint(tmpdir + "/test_ckpt_for_fsspec/hpc_ckpt.ckpt")
-        else:
+            ),
+        ):
+            trainer.save_checkpoint(tmpdir + "/test_ckpt_for_fsspec/hpc_ckpt.ckpt")
+    else:
+        # New fsspec handles the cross-device fallback internally, so only `os.rename` needs
+        # mocking. Do not mock `os.chmod` here: fsspec's transaction commit calls it directly
+        # to fix up permissions after the copy, and a global mock would leak into that call.
+        with mock.patch("os.rename", side_effect=OSError(errno.EXDEV, "Invalid cross-device link")):
             trainer.save_checkpoint(tmpdir + "/test_ckpt_for_fsspec/hpc_ckpt.ckpt")