As already mentioned several times before, since the FAA is a member of the ICAO (International Civil Aviation Organization) as well as Egypt is, there is NO need to transfer it to an ICAO license, since both countries are ICAO members, like pretty much all other countries of the world, except Westsahara (Africa) and a few little islands in the Pacific. Recommend to read the following link:
International Civil Aviation Organization - Wikipedia, the free encyclopedia
What you're talking about is the conversion of the FAA license to the respective national Egyptian license! And in order to get this cleared you must get in contact with the NAA (National Aviation Authority) of Egypt, they will be able to answer your question(s).