"The condition necessary for the act of recollection, is the identity of the being who remembers, with that being whose former states are recalled by memory. To remember experiences of another would be to remember having been somebody else: in other words, to simultaneously affirm and deny one's own identity, a pure and absurd contradiction" (Amédée de Margerie, cited by Michael Maher in "Psychology")
How do I know that the subject of my memories and me are the same person? I have a memory of waking up this morning. How do I know that the subject who woke up, and the subject remembering it, are the same person?
I think I might have come across the beginning of an "argument" for the sameness of the subject that remembers some event and the subject that experienced that event.
Let's start with a principle that says that to feel or sense what Jack feels or senses, you have to be Jack. Well, when you remember some event, you remember the sensations felt by the subject of that first person experience. So, you seem to remember being someone else. But I don't really know how to develop the argument from here.