Hola Natterjack /
xxx
Essentially, there is NO such thing as "converting" a JAA licence to a US/FAA certificate. No wonder schools do not know what you talk about.
xxx
So, if you wish to obtain a FAA certificate, if you would please state your current licence/ratings and flight time, and tell us what you would like to obtain as a certificate, we could tell you what to do... but it is not "converting"...
xxx
If you want the issuance of a "special purpose" certificate (stating that your JAA pilot licence is validated for the US/FAA), you can obtain that,
without a test for VFR only, not usable for commercial flying... If you want the I/R privileges, you must pass the FAA Instrument written test (but still not valid for commercial flying) -
xxx
So, if you tell me a little more, I can answer you a lot more...
xxx
Happy contrails