Full Acknowledgement of Broadcast
This is the equivalent of saying 10-4 in today's world. It's just a quick, easy, cool way to say you understand and you're moving out. Yup.
FAB stands for full acknowledgement of broadcast, which is similar to the police phrase 10-4. It may also mean final audio broadcast, fully acknowledged broadcast, or fully advised and briefed.
In this very popular British TV Show Thunderbirds from the 60s FAB stood for Full Acknowledgement of Broadcast. The producer Gerry Anderson was know to come up with some catchy phrases on this show.He set a trend back then for phrases like that. This was one of the really grat shows back then.