So I have a project area where we have the ability to modify the structure locked down, the delete permission is turned off across the board as if the ability to "Save Folder" for Administrator and Author roles .  We have therefore created a new role for those privileged enough to at least have Folder capabilities .. so the new role is "folders" and the permission set is Create and Modify only.

However, when logged in as a user with this role assigned to them in additional to Administrator and/or Author, they can create a folder, but cannot delete it (as expected) but neither can they move the folder elsewhere ... so what permission is required to allow the user to "move" the folder or is that somewhat internally considered deleting and recreating elsewhere ?