Schnellinger, Netzer, Breitner, Rummenigge, Kohler, Brehme, Littbarski, Häßler, Förster, Schuster, Stielike, Briegel, Klinsmann, Völler, Möller, Effenberg, Sammer, Reuter, Berthold and many more. Hardly any of the great German players of the 80's and 90's didn't play abroad actually.
Even today besides the obvious ones you also have the likes of Rüdiger, Mustafi, Gomez, Podolski, Mertesacker, Marin, Schürrle, Boateng and more who moved abroad/still are abroad. And that's only the ones who were capped for the nationalteam. The list is very long.
German mother, Tunisian father, born in Germany and lived and learned playing football in Germany. It's stupid to put an asterisk on it, he's simply German.