Kakeru gives Naho a hairpin. And on the weekend, Kakeru invites Naho to study with him for the upcoming exams. As the pair begin to grow closer together, Naho gets up the courage to invite Kakeru to see the fireworks together with her at the end of the school festival.
So the contents of the letter 
should change, as well.
Dann müsste sich
auch der Brief verändern.
Pareil pour la lettre.
Тогда и письмо должно измениться.