@Darklight99 If I were to get your memories, would I be you? No. There is a process of metabolizing memories and combining them in unique structures that help makes us who we are. Someone might remember getting caught in a great rainstorm that quickly drenched them utterly and cursed their luck, another person might view it as great fun. There is a dialogue between memories that tie them together. You can't just plop a completely different dialogue on top and call it a day.
Let me ask you this, if you took two books and mixed them together so sentences are randomly from one book or the other, is it still the original book? But all the words and information of that original book is still there.
Or lets say you took a loving saintly person who's always cared about others deeply, and gave them the memories of a serial killer, would they be that person? No, they'd be a traumatized nice person (most likely IMO)
As near as I can tell this comic is using the wifes dialogue, and just has only the memories before she turned 8 (or was it 10?) So the little girl who existed before this could be thought of as dead, the being that awoke to their old memories replaced it.
Really though what I suspect is this is the typical asian concept of reincarnation, that someone is themselves even with no memories from that self. The buddhist view of reincarnation as buddhism has mixed in with chinese culture to a degree. So I'm sure from the authors perspective, the little girl was the dead wife both before and after remembering. My philosophy of self and ego doesn't see it that way.