If you are truly done, there's no need to tell her about it. You'd simply not care. The fact that you are even thinking about a letter tells me you still have some attachment. If you had no attachment, you wouldn't even think of writing the letter.
Your W just moved out a month ago, Ty. I don't think you've dropped the rope yet.
Maybe your subconcsious is pushing you to make a move to avoid being in limbo.
I think your wisest move is holding off on doing anything right now.