JAA doesn't exist anymore. It is EASA now. Let's assume we are talking about converting from ICAO ATPL to EASA ATPL license.
You have to jump the following hoops.
EASA class 1 medical
You will have to do the 14 written exams. But, you don't have to go through an approved training course.
1500 hours flying time of which you must have fulfilled certain requirements such as 100hrs night, 500 multi crew etc etc.
You'll need to pass an ATPL Skills Test on the aircraft currently held in your ICAO ATPL
Someone else can come along and fill in the blanks.