I got an idea for the final plot twist:
The one who placed that letter should be Shouma who actually is into the MC!
Either that or Shouma placed that love letter to stir things up seeing how is friend is seemingly surrounded by lots of girls who got a thing for him but the MC does not notice it.
So then Shouma, to "help" his friend and advance his friend's private life to finally hook up with one of the girls, wrote that letter and put it into the MC's shoe locker.