Sorry Josep, but the argument will not be so conveniently ended.

"Reincarnation" is a religious concept. There is no scientific evidence for it.

"i. I exist, I am conscious, I experience."

This is because apparently mankind can interpret his existence through the
use of his brain.

ii. I remember existing and being conscious and experiencing.

Only to a certain degree. You can't remember existing thousands of years ago. You can however make it up but this would be madness if you believed it.

iii. If I (someday) recall an experience, then I was conscious of and during that experience. I was conscious at all the points I will (someday) ultimately remember.

Not necessarily. The mind or brain sometimes malfunctions. Memory is erased.
Sometimes entirely.

"There is no presupposing the conclusion that death cannot extinguish consciousness, it arises as a natural, logical fact when one takes the three statements above to their logical ends. Since they seem to be be a priori, my argument holds. It is not a matter of belief."

Your hypothesis doesn't hold. Death distinguishes consciousness for the dead.
Others may have consciousness while they are alive but there is no universal
consciousness. This has never been proven.

Philosophy is a strange subject. It is often manipulated by symbols such as in the Vienna Circle. The problem with it is that there are always counter arguments to those postulated. The "absolutes" are shibboleths that are destroyed by later philosophers.
This has been the history of a priori arguments.

With science, we see a flexibility that doesn't deal in absolutes but requires continuous verification. "Consciousness" has never been truly defined away from those who claim it.