Maybe I wasn't clear enough.
Lets say I ahve a form like this:

And obviously I can edit the dependencies.

Now I'm moving the SelectionTest from ForThisBlock folder into ForThisSite (or other shared block folder) it looks like this:

Of course the form looks the same as above after this action

And the Select dependent field window is empty as above.

Do you have any ideas if this can be fixed? One workaround is to move the selection block back to for this block and edit it, and then move it. But it is not intuitive :)