Move shared note to shared folder with same people in Apple Notes

In Apple Notes, is it possible to move a note that is shared with a group of users into a folder shared with the same group? I cannot seem to do it, but the UI isn't explicit about why it is failing. When I drag-and-drop the note into the folder, the folder is not greyed out and the drop seems to succeed. However, the note does not move. I have tried on both MacOS and iOS.