I got a riding mower question read description?

I have a briggs and stratton 11hp engine and the stator is dead. now i have this older kohler 10hp cast iron engine and was wondering if i could swap stators? if not i will buy a new one, i just don't want to have to buy one unless i have too. Also what would be wrong with the stator if it can run the headlights but not charge the battery at all!!