Did any of you see the Richard Gere/Jodie Foster movie "Sommersby"? It was about a man who had been missing in the US Civil War returning home to his wife and kid. (it was based on a French story, I think there was a French movie, too)
Anyway, he came home and his wife welcomed him. But the guy she'd been dating thinking her husband was dead did not believe it was really him- the dog didn't remember him, his shoes were the wrong size, and other things that made him suspicious. It turned out he wasn't really the husband, but a guy pretending to be him to get the wife and the farm. The wife, who had not gotten along with her real husband, welcomed and accepted this handsome stranger.
As it turned out, her real husband had been wanted for murder, and the law caught up with him, put him on trial and wanted him hanged. But those who knew he was really faking told him, all you have to do is prove you are not really Sommersby and you can go free. But his life before he "became" Sommersby had been sad and miserable, and he was thought of as a loser among those who knew him. As "Sommersby" he was loved, by the wife, and the neighbors and friends he helped. So he decided to die as Sommersby and leave a good memory rather than admit he was lying and was the other guy with an embarrassing past.
Okay now the AA connection. I have said that I believe in time AA believed she was AN, but in the beginning she probably didn't, she was trying to become her because she didn't want to be FS. Even FS's family was quoted as saying they 'left her to what she wanted, to be Anastasia." So they didn't want to spoil it for her, or take responsibility for her. FS had a miserable life and no future, but as Anastasia, even a fake one, she was loved by supporters, always given a place to stay by someone, she had fame and attention and adoration, so she left FS in the past and assumed this more popular persona. In time, her age and mental problems compounded and she really believed herself to be AN (IMO)