engine with ecm. swap 2001 golf to 2001 jetta

i'm buying a 2001 golf with a custom tune and modified engine to swap into my 2001 jetta, would there be any problems i may run into? i dont think the immobilizer has been disabled, but i can program it to my key with vagcom as far as i know could anyone verify this to be true assuming they have the same version 2 of the immobilizer????
thanks in advance fellas.....

now that i have more information could someone chime in ?????
so the golf is a german built 2000 car has immobilizer 2
and the jetta is 2001 mexican build with immobilizer 2 can i switch ecm's????