How did post transfer between enemies?

Short answer, it didn't, not ordinary private or business mail anyway. Postal service was suspended as soon as war broke out.

POW's however were covered by the various Geneva conventions, and they had the right to send and receive mail via the International Red Cross- it would have travelled via Switzerland or some other neutral country. Letters went from simple postcards announcing you were not dead but captured- like this to letters to your family, even to your favourite film star!

Civilians could only make enquiries about family in enemy countries via the ICRC - on a form such as was posted in this /r/whatisthisthing thread last year.

To give a TLDR, that was a Jewish refugee in England enquiring about her mother back in Germany- and getting the answer that she was in the Lodz ghetto.(And she eventually died in Auschwitz according to a post in the thread).

Source page for the POW postcard is here there are many other examples there.