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Since the sketchbook time-traveled with Sammy the second time but not the first, the sketchbook Professor Oak has at the end is 80 years old.
This also means that now there are two versions of the sketchbook that exist in the past, the 80-year-old one that went back in time and the 40-year-old one that became the 80-year-old one.
This movie causes a causal loop and a grandfather paradox. Since Sammy went 40 years ahead in time with no certainty of getting back, an alternate timeline exists in which he never returned to his time to become Professor Oak as we know him. Even though he does succeed in going back, this makes Ash and Pikachu's pairing either a coincidence or intentional manipulation on Oak's part. In either case, there is a paradox in which Oak could not have conceived of giving Pikachu to Ash without having met them as a boy, and Ash could have never owned Pikachu if this didn't happen (unless it was a coincidence). In other words, Ash received Pikachu because Oak met him as a boy, went back to his time, and then 40 years later gave Ash a Pikachu with which to meet his younger self.
It should also be mentioned that by comparing Sammy's sketchbook to the Pokédex, which didn't exist 40 years into the past, Ash could've actually given Professor Oak the idea for its concept, which one day possibly led to its creation. If this is the case, it would mean that the idea for the Pokédex came out of nowhere, resulting in yet another time paradox.
