Tin..
I don't believe that the CFI (initial) must be taken with FAA anymore.
Pre 9/11, yes...but Orlando (which does more of them than any other regional office) has closed down it's entire testing facility and put the testing back out to industry guys.
Miami and Tampa have done the same. CFI testing (unfortunately) back to the local examiners.
Was also told (may not be true) that the FAA does NOT keep records of written tests...copies of lost certificates must be obtained from the Company that set the exam...not the individual school where you took the exam...but the exam board - LaserGrade, Sylvan, Cats..etc.