I don't agree with any of that.
We may start with person A. With a split we may have persons B & C. Then with a rejoining we may have person D. Person A, B & C gone forever.
We cannot say what and how memory may be effected by any of this. Memory is not some perfect recording. It is tied to "personhood".
Yes, that's one way to look at it. Under that interpretation, however, it seems odd that a person exists (D) who has just as much access to the physical and psychological "history" of A, B, and C as you have to the last hour of your life up until now, but she is not the same person as A, B, or C.
It would mean that your brain can remain alive, functional, and capable of generating the conscious experience of being you, but you could somehow be gone forever. I'm not saying you're definitely wrong, just that it goes against some of my intuitions about self-preservation and continuity.
Of course, the conclusion of my argument goes against other intuitions. In the end, one has to decide which intuitions are worth keeping.
I would maintain that there is no reason to suspect that someone with the same brain I had yesterday and adequate memories of the intervening experience is somehow a mysterious, new consciousness embodied in what used to be my brain, even if the intervening experience included splitting and rejoining my brain. As long as it wasn't destroyed or deprived of too much oxygen, it should still be the same brain I always had.
But the broader conclusion of this argument is that brains don't matter, because the same splitting and fusing could be imagined with entire brains, not parts of a single brain.
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Hmmm... memory?
Memories of the mammory?
How old are you?