I think that, unfortunately, things are not that easy. You have to finish your training with the same CAA you started it and passed your medical.
Even if the JAA is pretty much a "standartized standard" every country might have it's little differences and a different interpretation of the regulations.
I don't have the JAR-FCL reference here, sorry for being so vague, but this has been a helluva week and I got a brain like glue tonight.
