Possible solution to the personal identity problem I think your terms a little muddled here but i could be fully misunderstanding you.
I believe you're referring to what Parfit thinks 'matters' after deciding there's no such thing as personal identity. Which is to say, the psychological continuity is what matters, and that your actual identity (i.e the state of being identical with oneself) isn't important.
I take that to be somewhat a way to comfort himself after realizing we may not actually 'be' any 'one'. Which is daunting to some degree, i feel.