The six-minute long cartoon fantasy Wide Prairie - about a child riding a prairie on horseback - was shown as part of the Edinbrugh International Film Festival before the British première of Robert Redford's The Horse Whisperer.
Sir Paul McCartney was not at the screening - he was taking his first family holiday since his wife's death from cancer four months ago.
Festival producer Ginnie Atkinson, dedicating the night to her memory, told a packed auditorium Sir Paul told her Linda would have been happy to see her film make its debut at the festival.
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Echoes her last words
The film uses bright cartoon images to tell the story of a woman waiting at an airport for a flight from Paris, dreaming of how she rode on horseback through the American West with her mother and father as a child.
Later, she rides off with a dream lover, all set to a country-and-western style song composed by Linda.
The film echoes the last words of Sir Paul as his wife lay dying.
He told her: "You're up on your beautiful Appaloosa stallion. It's a fine spring day, we're riding out through the woods."
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Inspired by memories
Argentinian animator Oscar Grillo, who worked with Linda on the film, said the film was inspired by her own childhood memories.
"She told me stories about when she was a young girl with horses. She had many evocative memories and she loved horses.
She wanted to make a film about freedom, having fresh air in your face," he explained. He said she didn't let on how seriously ill she was, adding: "She was always such a positive thinker. She wanted it to be her healing film."
Mr Grillo, a friend of Linda's for 20 years, had worked on two other films with her and plans to make a fourth, also based on one of her songs.
"I think it's a dynamite piece, really powerful stuff," he added.