It's not you. It's a clone of you. "You" and your "soul" died the minute the process started and in its place is now an imposter that thinks everything is fine and dandy. Soul didn't transfer. New soul was created.
I can't tell if people are purposely misinterpreting this because you used the word "soul", but whatever. I would liken it to being put on anesthetics and never realizing you ever woke up.