Here is what TORn had to say:
“As readers of The Hobbit know, the tale of The Downfall of The Lord of the Rings and The Hobbit or There and Back Again, are contained in the fictional Red Book of Westmarch. In Peter Jackson’s LOTR films, the books are shown on screen and written in by Bilbo and Frodo and handed off to Sam Gamgee. (Not explained on film are Sam’s progeny later having the book and being Wardens of the Westmarch — hence the book’s title.) The fictional book, and either the telling from it or the reading of it, will establish Frodo in the films experiencing Bilbo’s story. Viewers to learn the tale of The Hobbit with a familiar Frodo getting the tale as well.”