Ugh I usually hate the whole replacement concept - as if someone has the same personality just because they have the same face! Especially when the person being replaced is dead, and therefore becomes somehow 'sanctified'. However, in this case, I want to read this just because it sounds like it might be an interesting foray into the psychology of the characters involved. So ignore the crappy concept and its glossed over non-resolution, and enjoy the characterisation and psychological aspect.
Dakedo, Ashita no Hanashi o Shiyou