Again, the Rockstar Games Social Club website is a big help for this one, to keep track of what you already have.

Letter Scraps can be collected from the beginning of the game and across all three available characters. If you collected them all, you will trigger a new small mission called "A Starlet in Vinewood". That mission can only be done by Franklin.

Be sure to save your game after collecting something with your mobile phone in the case you die!
 

All Letter Scraps Video Guide

A little tip if you start the final mission "A Starlet in Vinewood": Before you go to the mission marker near the entrance of a mansion, be sure to shoot the tires of the car in the driveway (preferably with a silenced gun) and park your own car not too far away. That will speed up things for you.