Also is it easy to convert a JAA PPL H to an FAA (H)?
It's easy. File a form and send it or fax it to the FAA, together with copies of your documents. They will check you JAA PPL(H) status with your CCA. You should decide in which FAA FSDO you want to be issued your FAA PPL(H) and state so in the form. They do not send it by mail so you'll have to show there. You should allow at least 90 days for processing.
There are an aditional requirements for UK applicants though...take a look.
Airmen Certification: Verify the Authenticity of a Foreign License, Rating, or Medical Certification