While reading another question I was reminded of a TV show or Movie I recall seeing (Strongly suspect it was a TV show, maybe one of the recent Twilight Zone series or Outer Limits type shows.
An Impersonator of a famous singer or movie star (i.e. Elvis impersonator or Charlie Chaplin, Marilyn Monroe etc.) somehow goes back in time to meet his idol.
And while talking with the original, the impersonator upsets the original. [maybe telling him/her to do something different that he/she had done in the future, (maybe so he would not die?)] They end up fighting, with the impersonator accidently killing the original. So the impersonator takes over the original's life.
I seem to recall that the impersonator now years later is giving an interview to a reporter and has been telling him this story ending it with something like "I hope I have been able to live his/her life as he/she would have wanted to live it"
I also think that the original had died early in his career but that the impersonator had avoided that fate and allowed him to last much longer. (Matching the time line WE know)
I am pretty sure the original and impersonator were male characters, but they might have been female.