Roger Penrose did not say your soul is eternal. That second sentence is doing work the first one never authorised.
Penrose's actual position is considerably more careful and considerably more interesting. His argument, developed with anaesthesiologist Stuart Hameroff into the Orchestrated Objective Reduction theory, is that consciousness may arise from quantum processes inside structures called microtubules within neurons. When the brain dies, he proposes, the quantum information that constituted conscious experience does not simply vanish. It may disperse into the fabric of spacetime itself.
This is meaningfully different from claiming the soul is eternal.
The conservation of matter principle the post leans on is real physics. Mass and energy cannot be created or destroyed, only converted. Every atom that built you existed before you and will exist after. The carbon in your bones was forged in a star that died billions of years before Earth formed. When you die those atoms will become soil, then grass, then something that eats grass, then something else entirely, for as long as the universe runs.
But conservation of matter says nothing about the persistence of the pattern those atoms formed. A library burns down and the atoms in the books survive perfectly. The information in them does not.
Whether consciousness is more like the atoms or more like the information is the question Penrose spent his career trying to answer. He does not claim to have solved it. The post has him solving something he explicitly said remains unsolved.
The actual question is harder and stranger than the answer being offered here. Which is usually how it goes with Penrose.