Did Lara Jean and Peter get together in the book like they did in the movie? If so, how?

It is implied at the end of To All the Boys I've Loved Before that Lara Jean and Peter get together. However, the first book in the trilogy isn't the end of the story and doesn't coincide with the end of the film.
At the end of the first book in the trilogy, Lara Jean decides to write a love letter to Peter. She's realized she's in love with him and wants to be with him. Their story picks up in the next book, called P.S. I Still Love You. That has some scenes from the movie, like the hot tub during the school trip and people sharing a video of Lara Jean and Peter. At the end of that book, though, she takes him back after a breakup.
At the end of the third book in the trilogy, which is called Always and Forever, Lara Jean, Lara Jean and Peter end up together. They decide to be in a relationship even after they go away to college. She thinks that when she tells people how they got together, she'll tell them it started with a love letter.