Hola suus1983 -
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With your JAR Commercial, you can go to any FAA office, and request a FAA Commercial pilot certificate, that you will obtain immediately. The certificate will state -
"Commercial Pilot
"Airplanes single and multiengine land
"VFR privileges only
"Issued on basis of JAA (country) Commercial pilot licence nºxxxxx
"Not valid for hire or commercial operations of airplanes...
"Expires (date)...
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Note that your JAA licence must be valid (medical as well) when you fly with such FAA certificate.
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If you wish to validate your JAR instrument privileges, you must pass a test (takes a couple of hours at worst) which is a "foreign instrument rating competency test"... see FAR 61...
There is no FAA equivalent of a JAR fATPL, so you get a Commercial certificate.
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Happy contrails