Two minor points here:
The FAA is not authorised to
convert foreign licences. It is authorised to issue a certificate on the basis of a foreign license (
14 CFR 61: § 61.75, 61.77, 61.123 (h), 61.153(d)(3).)
The UK CAA does not
issue flight crew licences but rather it
grants them. JAR-FCL makes reference to
issuing licences.
Furthermore 14 CFR 61,
§ 61.75(b)(4) ['...applicant for piggyback private pilot certificate...'] "Holds a current medical certificate issued under part 67 of this chapter or a current medical certificate
issued by the country that issued the person's foreign pilot license."