Don't really know where I stand on the idea of reincarnation. Personally I believe that when we die we just end. That's it. Nothing.
I'm prompted by a theory of sorts: If you built a mechanical man and it had an off switch, we would not see it as being dead should we use that switch as we can of course turn it back on. It's not really alive.
However, let's go forward a few hundred years. Our mechanical man has had countless upgrades and improvements. Biological parts replace the mechanical ones. Eventually we can no longer tell the difference between him and us. We "know" he's not real because we "built him", yet when we go to switch him off he now pleads to be kept "alive" and fears the "death" that would follow with his termination. As he is now mostly biological such a shutdown would indeed be irreversible.
Is this entity alive? Would his "spirit" go on?
My point is that simply because we are biological beings doesn't really mean we are truly alive. It's quite a concept but goes along the lines that believing you are a living thing is merely a property of being a biological entity. When the biology stops, the biological machine has merely shutdown.
Having said all that, how come I have memories that are not my own? I once voiced these memories to my mother who turned white as I told her. She then told me of my brother who had died some years before I was even born. What I was remembering were his memories. I didn't even know I had a brother.