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It wasn't part of the theatrical movie in Japan. Prior to the movie being released in Japanese theaters, there were a series of radio dramas telling background stories for the events leading up to Mewtwo. Early next year, the movie was released on home video and the radio drama episodes were on a CD. Halfway into the year, they created the special "kanzenban" (perfect version) release of the movie on home video which appended a short animated adaptation of some parts of the radio drama to the beginning of the movie. It also changed numerous smaller aspects of the movie like turning a bunch of traditional 2D animation into CG (ie. the big doors). This kanzenban version of the movie was the one used as the basis for all international releases, the original version is pretty obscure. However, international releases omitted the Birth of Mewtwo addition to keep the movie around its Japanese length since it already had the Pikachu special at the start.
The special was finally officially released in English with the DVD release of Mewtwo Returns in the special features menu.