There's no direct conversion (there is for Canadians, but that's not JAA). If you have the JAA ATP you'll meet the minimum flight time requirements. You'll have to pass the written and a checkride. Your types won't "cross over", except for the one you take the checkride in. I'm away from home and don't have my "library" so there may be additional details, but these are the high points. You can contact Pan Am, Higher Power, or the like and they can give you better information. Twin Wasp's notation of 14 CFR 61.153 is the applicable reg.