Iron Sky/WMG

Fegelein is behind the invasion.
That's where he kept running off to, and the source of all his pranks.

FEGELEIN! FEGELEIN! FEGELEIN!!!

Hitler himself will return at the end of the film.
No Nazi film is complete without Hitler. Cloned him, time-travel, ascended to a higher plane of existence? Space Nazis will find a way.

The movie is an alternate timeline of Nazi Zombies
In this timeline the zombies were controllable by their living officers as a result the Nazis had completed their moon base before the Allies inevitable crushing of the Third Reich, as the zombies did not cause a breakout