Rinne no Lagrange: Kamogawa Days / 輪廻のラグランジェ 鴨川デイズ

As Yoko has her assistant scour the seabed in search of something, Madoka, unable to pilot Midori properly again, returns to Kamogawa to see the New Year in. Upon returning home, Madoka receives New Year's letters from Lan and Muginami, updating her about what's going on in their lives, to which Madoka makes a prompt reply. As the months pass by and Madoka moves up a year in school, Lan and Muginami visit an intergalactic replica of Kamogawa on the tourist planet Polyhedron. Takes place between seasons 1 and 2. (Source: Wikipedia)...