It's immediate once you take delivery. The transfer happens and then it's not longer available on the previous car. We transferred from our M3. While I was looking over the MXP, my wife left with the M3 to do her errands. Once I took delivery, FSD was no longer available on the M3 while my wife was on her errands (and she uses FSD constantly). When she came home, said FSD wasn't working on the M3 anymore (basically implying she didn't want to drive the M3 anymore)
This is the email I received almost immediately after hitting the accept delivery in the Tesla mobile app