FAA............
ICAO states any way does not recognize FAA, only the flying done on the a/c.
That too if it is genuine not just logging(plenty of cases), that’s the reason when some body applies for CPL he has to go through all exams and medical as prescribed by the state.
All coming for license ISSUE in ICAO states have to pass local test and medicals.
It’s only in INDIA that pilots can fly on with medical fitness certificate issued by other states(genuine or forged no body knows) on FATA which is special clearance given on the discretion of DG.
due to the D.G. they don"t have to do RTR and MEDICALS in the state.