Montresor concludes his narrative with these words:
Against the new masonry I reerected the old rampart of bones. For the half of a century no mortal has disturbed them.
In pace requiescat!
So fifty years had passed before Montresor was ready to tell his tale. There are various theories about the person to whom he is telling it and the means of communication. He would be pretty old after fifty years and could be making a deathbed confession. However, it seems more likely, because of all the details in the story, that he was writing it down with the intention of sending it to someone whom he addresses at the beginning as "You, who so well know the nature of my soul."
Since the story was published by Edgar Allan Poe in an American magazine in 1846 (see reference link to enotes introduction below), it seems likely that Poe's fiction is that he is offering a translation of an older document written in French or Italian which somehow or other came into his hands. That would mean that the story in English was being offered more than fifty years after the fictitious event, and Montresor is certainly dead.
Perhaps Montresor is supposed to have penned his confidential confession but never entrusted it to the mail. The original hand-written manuscript might have been found among his papers after his death. He would not be the first person to have written a highly confidential letter and then decided not to send it. Or, perhaps it could have been found among the papers of the man or woman who received the letter.
Poe experimented with various narrative devices. One ingenious device was the narrative in his story "Ms. Found in a Bottle," in which the entire harrowing tale was supposedly written by a sailor in supreme peril on the high seas and tossed overboard sealed in a bottle, to be discovered eventually and published in a magazine.