This ties into Hana no Mizo Shiru and tells the professor and Misaki's grandfather's story. It will probably make you cry. Misaki and Arikawa are in this as well, and we get a little relationship development to make up for the tragedy in the first chapter.
ETA: Maybe they saw one another while Akira was still alive, after his wife had passed. I like to think they wrote each other letters and remained good friends, and maybe even stole away for time together sometimes, hopefully with the full knowledge of their partners.
Hana No Miyako De