This page explains in detail the interactions between the Final Fantasy series and The Matrix series.
The Animatrix[]
June 03, 2003
Final Fantasy
The Matrix
Aki Ross in The Matrix
The special features of The Animatrix DVD include an interview with the creators of "Final Flight of the Osiris" short, and during that, a clip is shown featuring Aki from Final Fantasy: the Spirits Within fighting a sentinel. This clip was made as a simple test by Square Pictures using a sentinel model Warner Bros. sent them, and the model of Aki from the Final Fantasy movie. Aki's hair was made short and her suit was recolored to look like leather.
Note that the character in the movie may not be considered Aki, but rather a girl looking like her (making this only a Type 3 or out-universe reference), since in the clip she shows fighting abilities not from the original movie, and having a different haircut makes her different after all.
We decided to consider her an actual Aki because the creators had the right to use the actual character, so unless she's named otherwise, we can consider her a different version of Aki, but still her.
License[]
"Final Flight of the Osiris" was created by Square Pictures, that also created Final Fantasy: The Spirits Within and specifically the character Aki, so they were freely able to use her in their clip and sending it to Warner Bros. autorized them to use it in the Animatrix DVD.