Okay think about it like this. Remus was best friends with James for their entire Hogwarts education. Was probably at the wedding between James and Lily. He, James, Sirius and Peter were the best of friends till the Potters were killed by Voldemort.

Remus, like everyone else, thinks that Sirius betrayed the Potters and that Peter is dead. However, Harry is alive.

The son, and only link, to his dead friends is alive. What does Remus do? Who the fuck knows but it definitely didn't have anything to do with Harry.

When Remus became a professor at Hogwarts, one would think that (especially after giving Harry lessons on casting the Patronus) he would reveal that he knew Harry's parents more than many others. That he might've sat Harry down and told him stories about his parents.

>inb4 tl:dr