I'm happy to help you get started on that letter. I can't write it for you though; Enotes frowns upon that kind of thing. The story starts out with this line:
"THE thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge."
That tells you that Fortunato is likely a "user." He uses his friends and acquaintances to his personal benefit. It could also be that Montresor is completely ignorant of how his actions hurt people around him. I doubt that Fortunato is actually physically injuring Montresor, so the injuries that Montresor is talking about are likely emotional injuries.
Whatever Fortunato has been doing to Montresor is bad enough for Montresor to commit murder. What would cause someone to seek murder? I'm going to go with love. I would focus your letter on how Fortunato knowingly or unknowingly stole the affections of a woman (or more than one woman) from Montresor to himself. Perhaps one of Fortunato's sexual conquests was a family member of Montresor's. The text doesn't indicate that Montresor has any family, but it also doesn't say that he doesn't have a family.
The love angle could be your first set of injuries. Another set of injuries could be business related. Perhaps both men compete for the same kind of client base. Or maybe they were business partners at one time, and Fortunato ended up somehow hurting their partnership or lost a lot of money.
My last recommendation is to think about yourself. What would make you so mad at a friend of yours to consider seriously hurting them back? Write about that.
I would base the letter on your own reality. Write it confessing controversies worthy of being killed over. Hot topics are usually, love, friendship, family, truth, religion, and money.
Stylistically you could write it in a very sarcastic "sorry", slightly bragging way to further your point the the atrocities committed deserved the consequences Fortunato received.