In the novelization it says that Jean survived the wave by creating a psychic cocoon, what if Jean was able to do something similar for scott, to protect him from the pheonix part of herself, and to be sure he is kept safe considering how it was the pheonix, I think that called him to the lake she erases it from her own memory so the pheonix will not know he is still alive, and when everyone tells her, logan first and Professor X later that he is dead she just assumes they are telling her the truth, I mean all logan found was the glasses, and if the psychic cocoon was strong enough to make the professor think Jean had died, he would not be able to detect scott either, and after the alcatraz incident the shield falls apart and he wakes up, underneath alkalai lake and swims to the surface, and then maybe have him wander around canada for awhile before finding a ride and more or less hitchiking back to the school and they inform him of all that has transpired, with the professor and alcatraz. He take his position as field leader while storm stays on as headmaster of the school until the professor returns.