How do A and Rhiannon end their relationship in Every Day?

A and Rhiannon end their relationship when he says goodbye to her as Alexander and then wakes up in the body of Katie, intending to get as far away from Maryland as he can so he won't be tempted to go back to her.
A wakes in the body of Alexander Lin. He's a kind, thoughtful boy who is someone A immediately likes. It makes him want to stay in the world in the body of Alexander so that he can be with Rhiannon. He invites her to meet him.
They spend a day together, pretending they've just met. She doesn't understand why A wants to do that but goes along with it. They have a lovely date and at the end, A tells her that he knows how to stay but that he won't do it. It's murder.
She argues with him, but his mind is made up. He tells her Alexander will wake and remember her. He'll remember their beautiful day together. He tells her to give Alexander a chance and be happy with him. They go to sleep in each other's arms.
When A wakes up, he's in the body of Katie. He decides to get as far away from Maryland as possible.