Like I said, the edited save file does not load on the game.
PKHeX does load the edited save game perfectly fine, so that is not the Problem.
Plus I checked with Pokemon Y, same behavior. Plus since it's a save game, where I'm only 5 minutes into the game, I tested loading it on the cartridge, which is not working either.
Restoring the original save game was no Problem. So it really seems to be something about the PKHeX edited save game. I'll try an old version of PKHeX next, to see if it might be a problem with the newest version.
EDIT:
No, old version didn't change anything.