To the best of my knowledge for a JAA PPL you only need a radio licence in addition to your FAA PPL, no further training or checkride required.
The german authorities even have a standard form online to request the acceptance (not the transition!) of your FAA PPL.
Its kinda like FAA PART §61.75 "Private pilot certificate issued on the basis of a foreign licence".
I think there are two ways: transition or flying on the foreign licence; in JAA-land world I think you are required to fly a certain amount of hours during a period of time, if you don't, your licence expires and you'll start over again! When you get your FAA licence accepted, you can stop flying for years, take a (FAA) flight review, and ask for another "certificate issued on the basis of a foreign licence" from your local JAA authority.