Thanks for the info! I'm still not sure what I should be doing. I have got the schematics from the mopedriders.org site for both 12v and 6v but can't really understand the 12v one.
I have two mopeds, one is a 51v (28-04-78) and the other is a 51SU (30-05-79). I thought they were both 12v. I have put the engine from the 51v onto the frame of the 51su but I don't think that should make a difference. The headlight on the 51v was 6v but other globes said 12v, and all the globes on the 51 su are 12v.
As far as putting everything back to stock, that is my problem, it wasn't connected when I got the moped so I am kind of guessing. I sort of understand what you said, but could you please explain how I could put both the magneto coils in series? I would be eternally grateful if you could draw on my picture how I should have set it up with the headlight : )