I'm a little skeptical of the claim myself, hence the question. The main thing that bothers me about it being that I can't really see how the Germans could send letters to the USA while at war with them, considering these are physical things that would need to be transported on a boat or plane.
POW's had the right to send and receive mail due to the various Geneva Conventions that governed their treatment. This was handled via the International Committee of the Red Cross, so at some point the mail would have passed through Switzerland.
I posted a few examples in this thread from a few months ago
Of course this was true for US/British POWs in Germany/Italy and vice versa, I don't think things were so easy for prisoners of the Japanese, and it definitely was impossible between Germany and the USSR.