In the first paragraph of the story Montresor states:
At length I would be avenged; this was a point definitely, settled—but the very definitiveness with which it was resolved precluded the idea of risk.
This defines the problem or conflict. It is solely a question of executing his planned revenge. The whole story is about how Montresor lures Fortunato underground, walls him up, and leaves him to die. Montresor's conflict, or problem, is with his intended victim. He has to plan his revenge carefully and then execute it perfectly. His conflict is with a boisterous drunkard who has to be kept intoxicated and cunningly manipulated every step of the way to his place of execution. The conflict is resolved when Montresor finally guides Fortunato into the narrow recess, wraps the chains around his waist, and fastens the padlock.
Throwing the links about his waist, it was but the work of a few seconds to secure it. He was too much astounded to resist. Withdrawing the key I stepped back from the recess.
This is the climax. Fortunato is as good as dead. The conflict which began when Montresor encountered Fortunato up on the street is now resolved.