This is a good question, but a difficult one. Obviously the main conflict has to involve either one or both of the main characters, Jimmy and Bob. Bob does not seem to be experiencing any conflict. He wants to see his old friend. That is his motive. There does not appear to be any obstacle to his doing so. He tells the policeman, whom he doesn't recognize:
"But I know Jimmy will meet me here if he's alive, for he always was the truest, staunchest old chap in the world. He'll never forget. I came a thousand miles to stand in this door tonight, and it's worth it if my old partner turns up.”
So it would appear that the main conflict is Jimmy's, although we do not realize this until the end of the story because we did not realize that the cop was Jimmy himself. Jimmy must know that the man standing in the darkened doorway of the hardware store is his friend Bob. If there is any doubt, it is quickly dispelled when Bob says:
“It's all right, officer,” he said, reassuringly. “I'm just waiting for a friend. It's an appointment made twenty years ago."
Almost immediately Jimmy realizes that his old friend is also the man known to the Chicago police as 'Silky' Bob. In those days there was no way of sending a photograph or even a sketch by wire. But later we learn that all the information about 'Silky' Bob had been wired. We know it was a wire because the plainclothesman will tell Bob later:
Chicago thinks you may have dropped over our way and wires us she wants to have a chat with you.
Jimmy sees three things that would have been included in the wire that identifies Bob as the wanted man.
The man in the doorway struck a match and lit his cigar. The light showed a pale, square-jawed face with keen eyes, and a little white scar near his right eyebrow. His scarf pin was a large diamond, oddly set.
The wire would have included a general description of the wanted man. It would have emphasized that he had a little white scar near his right eyebrow, and it would have contained a more detailed description of his "oddly set" scarf pin. The fact that it was oddly set would be nearly conclusive identification. For example, the scarf pin might have had a large diamond in the center with a circle of rubies around it, or something equally distinctive. Furthermore:
The waiting man pulled out a handsome watch, the lids of it set with small diamonds.
This is a third identifying item which would have been included in the Chicago police telegraph wire.
Now Bob has an internal conflict: man against himself, friendship against duty. This is his old friend who has come a thousand miles to meet him and who speaks of him with great affection. Yet he is wanted by the Chicago police and Jimmy is a cop whose sworn duty it is to arrest Bob. We do not understand how that conflict was resolved until the very end of the story, when the plainclothes arresting officer hands Bob the note that reads:
Bob: I was at the appointed place on time. When you struck the match to light your cigar I saw it was the face of the man wanted in Chicago. Somehow I couldn't do it myself, so I went around and got a plainclothesman to do the job. JIMMY
Many students who have posted questions about this story with enotes have wanted to know whether Jimmy did the right thing, or what you or I would have done, or should have done, under the same circumstances. This seems to prove that most of us recognize that the main conflict in O. Henry's well-crafted story is Bob's internal conflict over whether to arrest his old friend or let him go. There would have been a big conflict between Jimmy and Bob if Jimmy had tried to make the arrest himself. But O. Henry keeps it an internal conflict by having Jimmy delegate the arrest to a fellow officer.