This is pretty good and it has a lot of Plot to work with... The question is, What happen to the life she stole? What about the girl family and friends? In the end it's not her true appearance or identity..
If you mean Ano Hito no I ni wa Boku ga Tarinai, while there are certainly similarities—a good-natured protagonist dates a well-meaning monster of a girl, possibly flying in the face of wisdom, despite the fact that she comes off as genuinely terrifying and otherworldly sometimes, hearts fly and feel-good feelings seem poised to win in the end—despite all that, the details and the tone and even the genre of the works seem noticeably different to me...
Unless you meant another upbeat series where the mc dates an eldritch monster, that is. In which case do tell, I'm apparently quite fond of these. :'p
I think the OP meant the life she stole as in, the identity and lifestyle she ostensibly took over. How did/would the people who knew the girl she replaced feel about the sudden personality change? That sort of thing.