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Mewtwo in the games was created by Mr. Fuji, who founded the lab in Cinnabar as Dr. Fuji. That's why the portrait there returns a surprised reaction from Red (boy) or Green (girl).
Cinnabar gym also has a photo of Fuji and Blaine "standing shoulder-to-shoulder with big grins".
In the Japanese versions, the abandoned mansion has journals written by someone who write down where he discovered Mew and how it "gave birth" to Mewtwo. The researcher lost control of Mewtwo and felt hopeless. In Faraway Island, the message has a remnant of a signature (ジ), which further hints at Fuji, who went there to return Mew to its home.
In the English versions, the journals mention a team of researchers instead that ended up succumbing to Mewtwo's vicious tendencies making him overpowered, allowing it to run away. The message in Faraway Island no longer has the signature ledtover but it hints at the last four months of the year, which could possibly mean that Fuji went there shortly after (September 6) he lost control of Mewtwo (September 1).
Do note that the Emerald event was only held in Japan.
