Hi,
The JAA licence has different licence numbers than the EASA licence.
You will have to apply for a new US licence before you go over as your old US licence will now be invalid.
I did mine last year after converting the JAA FCL licence for the new EASA as it's based on the original licence number.
It has something to do with the first prefixes. JAA started UK-------- EASA starts GBR---------
Hope this helps.