In and of itself it is not a problem to switch your contract to postpaid because it is already in effect, but here I have to point out the FairUse Policy.
"If a customer spends more days in another EU country than within the country in a period of 4 months and uses more minutes, SMS or data than within the country, a roaming surcharge may be charged."
That's the first problem. The second obstacle is that we no longer verify the contracts via post - but via Video-Ident.
Since it is not possible to specify a contractual partner address that is outside of Germany when booking, the video identification process naturally fails immediately.
Long story short, I was able to help the first user in this article because the contract is also used permanently in Germany and we could use Post-Ident, I could no longer help the second user because of the Video-Ident procedure (even if the card would be permanently booked into the German network) and now in your case I can't help either because we either don't get the card booked or the fair use policy applies after 4 months at the latest.