If he has a PhD, we can refer to it as "his PhD". You would use "his" if you knew he had one and were discussing where he obtained it.
You would use "a" if you are focusing on what he did in Germany. He did (studied towards) a PhD.
You would only use "the" if you are referring specifically to the PhD, for example if he has two degrees, perhaps a BA and a PhD, you could say that he did the BA in England and the PhD in Germany.