Don't close your German bank account just yet. This is the most common expensive mistake we see, and it's easy to avoid.
Keep the account and the direct debit running. Wait for the final invoice, usually four to eight weeks after the contract ends. Let it get paid. Then cancel the direct debit, and only after that close the account.
Doing it the other way round means the payment fails. German providers pass unpaid bills to collection agencies quickly, and sorting that out from another continent is difficult.
We put a line in the letter asking them to send every open invoice and your current balance to your email address. It's one of the more useful lines in the letter, because it brings anything outstanding to light while you can still pay it from a German account.