What proof do I need? Well, you could start by proving this:

She's the Final Sorceress.
Entirely unfounded. The Ultimania states a sorceress MUST give up her powers before dying, and since Rinoa has a regular lifespan, there MUST necessarily be a successor eventually. You have yet to demonstrate how there could NOT be a successor. You have also yet to give any good arguments as to why the sorceresses we fight in TC are not in the in the era between Rinoa and Ultimecia.

Ultimecia Reign is technically within their lifetime, there is no evidence of a Successor to Rinoa.
No, Ultimecia's reign is NOT within their lifetime. You have completely ignored Lagunas statement that "Ultimecia lives far in the future, where none of us can technically exist". That, the "many generations" and the several sorceresses we fight on the way to Ultimecia all demonstrate that Ultimecia clearly lives outside their lifetime.

You may as well try to convience me the validity that there is without a doubt a successor.
1. Laguna states explicitly that Ultimecia lives in a future where none of the party can technically exist, hence it's outside their lifetime.
2. If it's outside their lifetime, Rinoa must necessarily die of old age before Ultimecia's era.
3. As a sorceress, she MUST give up her powers before dying.
4. Hence, there must be a successor.

Simple.