hi
easiest way is during a new rating with an US TRTO
start the process at least 2 month before the TR:
search the faa.gov site for a special form: application for an US FAA ATP on basis of your FAA ATP (attention: NOT VALIDATION)
send this request form to the FSDO near to the TRTO incl cert. true copy of ATP and logbook
pass the FAA theory test either part 121 or 135
pass FAA medical
ask TRTO to perform two checkrides, 1 FAA and 1 JAA (
afaik combined FAA/JAA checkrides are no longer approved by FAA)
apply for FAA radiolicence online (and pay...)
receive your FAA licence
rgds
welle
edit: the above way applies, if you do not previosly hold a FAA licence (CPL, PPL etc..)
edit II: correct typos...
or search pprune - this question turns up here quite frequently