Like I originally said, if it were possible to prove to someone else you’d be able to put it into words. It’s just like being aware of your own sentience without being able to demonstrate it to others. What I am experiencing now is not just a memory waiting to happen. I can tell the difference between memory and experience and I can chain experiences without resorting to memory. Maybe not everyone can do that. The inner monologue thing was just an idea but probably not related.
But I can’t put to words what that chaining of active experience is like in a way that’s ever going to convince you I’m a thinking being with an awareness of self that dates to before 0800 this morning. The real question for me isn’t “how do I know I’m the same person?” but “why is it difficult for some people to know the same thing about themselves?”
ETA: Do you also have the same questions about whether you are a sentient being or do you accept “I know I am” as the answer because the only proof is through personal experience?