I found a "dirty" quick fix:

Simply comment out the "Disabled Group" in MoveEditorWindow.cs and change the iD manually after duplicating the move-file:

//EditorGUI.BeginDisabledGroup(true);
moveInfo.id = EditorGUILayout.TextField("Id:", moveInfo.id);
//EditorGUI.EndDisabledGroup();

However, I'm not sure if this will cause any other problems. Are the IDs registered somewhere?

The ids are used to link the animations from moves to the animation controller (Mecanim Control) and the animation maps. Previously, UFE would load the animations based on the move file, often causing conflicts.
UFE 2.6 has an issue right now where duplicated moves (Ctrl+D) get their ids duplicated.
There is a fix coming to this in the next update (2.6.1), but if you don't want to wait you can get it now through repository access. Your solution should do the job for now though. The important thing is that the ids are unique.

I've been doing it this way for the last few days and simply changed the IDs. So far I haven't had any problems. However, I cannot guarantee this. If it's not urgent, it's better to wait for the update

Of course, you have to make sure that the IDs are unique, because they are the new identifiers for the moves and must not be assigned twice.
In addition, the first thing you should do immediately after duplicating is change the ID and then adjust the rest of the settings.