Jyn was instrumental in inspiring The Rebellion gain a new fighting spirit and hope during the events of the film.
While we didn’t see Jyn Erso record any sort of message during the events of Rogue One, perhaps she left The Rebellion with a final message of hope before her passing.
News of Jyn’s death would presumably send shockwaves into the organization, but a farewell message could help keep The Rebellion alive until Luke Skywalker shows up on the scene with Han and Leia.
And it worked, as she and her motley crew of rebels were able to steal the plans for the original Death Star and send it to The Rebels before their untimely deaths.