Why would you want a FAA PPL based on your JAA PPL unless you intend to fly in the states?
Your student pilot cert doesn't really come into the equation as it only allows you to fly solo with the appropriate sign-offs from a CFI. You don't need the FAA form either, what you will need is the form from the CAA. They relieve you of about 35 quid (I think) tell the FAA that indeed your PPL is valid and then you nominate a FSDO office to collect your FAA PPL, thats issued and valid only with your JAA/CAA PPL. The FAA will also send you a letter of authenticity with the pick up details and this letter is only valid for 6 months. If that time expires then you'll need to start the whole process again. A lot of hassle unless you intend to fly over there
EDIT, the license the FSDO issue you is the temporary airmans cert. (white piece of paper) that you'll be able to fly on as soon as it's issued. After about 90 days they'll send you a funky credit card style FAA cert.