My impression is also that it would be much easier if the soon-to-be-ex-wife returned for a week to properly de-register (and start the proceedings for a divorce), cancel the rental agreement etc.pp.

In any case, I'd immediately seek the advice of a lawyer.

If your first thing is done, the second is not necessary.
OP mentioned no kids, separation/divorce should be an easy thing. Communication is the key.

There's also the question of what law will/should apply. They may be able to chose, especially if they're from the same country.

Once registered, the (soon ex-)wife may be able to file "there", in which case "there" law may apply. So OP may want to make sure he's the first to file.

IANAL, OP does want to get one.

One point is her residence/home at your address, which you can state no longer applies. The other is the permit lapsing after 6 months, which you have no authority over.

She has no permit, she doesn't need one.

She has a B permit.

I think the post referred to my example of the woman who was at our address not the OP's.

Yeah, I should have read the whole topic (which you sort of stole )