Mr. Fuji/Anime

Main series
Mr. Fuji as in the elder from Lavender Town hasn't appeared in the Pokémon anime series. However, evidence from the other media suggest that Dr. Fuji from Mewtwo Strikes Back is based on him. In the movie, Dr. Fuji was involved in the creation of, from which he did not survive due to Mewtwo's destruction of the lab where it was created.

Pokémon Origins
Mr. Fuji debuted in File 2: Cubone. Much like in the, he had gone to the Pokémon Tower after it was taken over by Team Rocket, trying to convince them to leave, but wound up as their hostage. After Team Rocket was driven out of the Pokémon Tower by, Mr. Fuji rewarded the young Pokémon Trainer with the Poké Flute and a pair of mysterious stones. When Red asked what the stones were for, Mr. Fuji told him that he would find out soon enough.

Mr. Fuji reappeared in File 4: Charizard, where his past as Dr. Fuji is revealed by Professor Oak soon after he concluded that the journals Red found at the were his. He explained that Dr. Fuji used to be dedicated to Pokémon researching, but after he discovered a, the subjects of his studies were dismissed, and the Doctor was trying to artificially create a. Despite their last names matching, Red was skeptical about both being the same person, but the Professor told him it was very likely, as Dr. Fuji did a research related to mysterious stones flowing with energy, like the ones that Mr. Fuji gave him.

Later, in their home at Lavender Town, Reina told Mr. Fuji about the rumors of an incredibly strong Pokémon seen in the Cerulean Cave. After hearing that the Pokémon is likely a Psychic type, he indicated that he knew the identity of this Pokémon. After hearing of Red heading to capture the mysterious Pokémon,, Mr. Fuji began to think about Red's possibilities to win the fight against it. During his thinking session, Red battled Mewtwo in the Cerulean Cave, and wound up getting almost all of his Pokémon defeated, leaving him with only his. While Charizard battled Mewtwo, Mr. Fuji understood that Red's only hope of victory lied within the stones he had given to him. The stones, revealed to be a Charizardite X and a Key Stone, gave Charizard strength to rise from the brink of defeat and Mega Evolve into Mega Charizard X. This new power gave Charizard the ability to defeat Mewtwo, allowing Red to it.