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Gaínza has been residing in Miami, Florida since 1979.
Originally he went by his father's surname of Stewart; the reason which led him to abandon it for his mother's maiden name, Gaínza, are closely related to his motive for going into exile.
Finding himself in disagreement with the political situation in Cuba, he made an attempt to escape to the United States by boat. This was and continues to be illegal, and having been apprehended by the Cuban authorities, he was sentenced to jail for two years in 1964.
Upon his release from prison, Gaínza pursued employment. However, due to his easily identifiable Anglo-Saxon name, the authorities had him turned away at once, in their discrimination of political dissenters. After being continually fired, he decided to use his mother's family name and continues to use it today. Thanks to his subterfuge he was able to find employment and return to school at San Alejandro Academy of The Arts.