Let's call my friend Bob and the story girl Alice.
Background
I was in class with Bob and Alice. Some day Bob posted a picture of a gun (not his; from the Darknet, because he was drunk) in our class chatroom (WhatsApp). A few days after, a policeman came into our classroom and took Bob outside. Later on, when he was back, I asked him what happened.
Bob recognized he did a wrong thing and apologized to the whole class. Please note that we've all known each other for more than 5 years, so we know he was drunk when he did it. The class took it as a joke, and we all moved on.
OK, now here's where things are getting pretty strange:
Problem
Bob was suspended for three days, apologized and accepted the punishment without any discussion. A few days after the talk with the police, a teacher went into our classroom and asked the whole class what they have to say about Bob's action. Everyone remained silent but Alice, who said Bob would kill everyone in the class and mentioned some things Bob has done several years ago to prove her right, like the fact that Bob used to throw firecrackers to the ground with another friend from the class. The problem is that Bob was legally throwing these firecrackers on New Year's Eve, so there was nothing harmful nor unsafe in his actions.
Literally the whole class told Alice she shouldn't have said such things. Bob never hurt her.
Once he came back from his suspension, Bob was told by the class what Alice said about him. To my surprise, he wasn't even angry. He just said that he totally understands Alice and that he's really sorry for the whole thing.
A couple of weeks after that, Bob got suspended again for three weeks for the "picture-class-story", and when he came back, Alice offered him to lend her notebooks for he can get the lessons missed during the suspension. Bob didn't ask anybody for borrowing notebooks, and she spontaneously offered hers.
About one month later after the “picture-class-story“, Alice claimed completely out of the blue that Bob has been following her on her way home (which isn't true, because he is always the first one to leave the class and goes home right after). The police came again, and Alice said something that really surprised the policeman :
Sorry, I see that this is impossible that Bob followed me. I withdraw my statement.
Alice's attitude toward Bob is very variable, going back and forth from positive to negative. She stares at him during breaks and she and a friend of hers even call him by a nickname. When a teacher was criticizing Bob and telling the class about their hatred toward him, Alice stood for him and defended him.
Bob eventually changed schools, and I asked Alice after that why she did this to him. She said she had nothing against him... and that she didn't even really talked to him once in her life!
Bob does not hold a grudge against her either, but wonders why Alice always want to get him in such trouble.
Alice asked me to help her reconcile with Bob.
Question
What can Alice try to do to reconcile with Bob after making false statements against him?