Unlike other GTA V collectibles, there are no special requirements or side missions necessary to make letter scraps appear--they can be collected at any time, even at the start of the story, and with any character. Note that some letter scraps require a helicopter to be obtained. Once all 50 letter scraps are collected, go to the green "Killer" question mark while playing as Franklin to meet Leonora Johnson's killer (Dreyfuss). You must kill him to get the "A Mystery, Solved" achievement/trophy.
View the following video to see the location of all 50 letter scraps in the game: