The predominant conflict in "After Twenty Years" is an internal one that is not apparent to the reader until the surprise ending of the story. This internal conflict arises between friendship and duty within the character of Jimmy Wells (Man vs. Self).
As is typical of O. Henry's stories, the narrative begins in a manner that causes the reader to be unsuspecting of the policeman's identity. He seems to be a man who is complacent in his role in society as he twirls his baton and checks doors to be sure that they are locked—"His impressiveness was habitual and not for show." Further, the policeman's conversation with the man in the doorway is noncommittal, as there is little indication that he may suspect the stranger's identity. Apparently, too, at the time of the setting of the story, police officers wore no name badges as they do nowadays or, perhaps, the stranger from the West may have identified Officer Wells as his old friend.
It is not until O. Henry's ironic reversal at the end of the narrative that "Silky" Bob becomes aware that his old friend Jimmy has been on time for their meeting. And, as he reads the letter from Jimmy, Bob learns of the internal conflict between the part of Jimmy that was his friend and the part that is a policeman on duty.