Pekka,
I think you are not able to "convert" a JAA CPL licence to FAA CPL or vice versa as there is no agreement between JAA and FAA for reckognising each other licences. On the other hand it should be quite easy for you to obtain a FAA CPL if you have a JAA CPL.
Check in the FAR AIM (Part 61 if I remember right)the requirements for applying for a FAA CPL and check if you already meet these qualifications ie. Dual, Solo and X-C flight time etc.
Then you need to study for the written exam, get a sign-off from a certified flight instructor for beeing able to do the written test. If you are going to do the flight test in an R22 you need to meet SFAR-73 and a sign-off from an certified instructor and he will probably sign you off for the CPL check ride as well if he is satisfied with your flying.
Hope this helped!!!
Good Luck