When does Jimmy figure out who the man from the west really is in "After Twenty Years" by O. Henry?
As soon as Jimmy sees Bob, he recognizes him as the wanted man, rather than his old friend.
In this story, two old friends make an arrangement to meet each other at a restaurant in twenty years. They do meet, but things do not go as planned. Jimmy and Bob have not seen each other for a long time. When Jimmy sees Bob, he does not immediately acknowledge him, but he does recognize him. He realizes he is a criminal.
Jimmy talks to Bob, pretending to be just another cop. He doesn’t acknowledge that he recognizes him as a wanted man from Chicago. He can’t bring himself to arrest his old friend. They chat, and then he walks off. He gets another cop to pretend to be him.
"...The old restaurant is gone, Bob. I wish it were here, so that we could have another dinner in it. Has the West been good to you?”
“It gave me everything I asked for. You’ve changed, Jimmy. I never thought you were so tall.”
“Oh, I grew a little after I was twenty.”
“Are you doing well in New York, Jimmy?”
Bob realizes that something is up because the man has a different kind of nose. He is a little upset at the charade. At this point, Bob is given a note from Jimmy explaining why he did what he did.
“Bob: I was at the place on time. I saw the face of the man wanted by Chicago cops. I didn’t want to arrest you myself. So I went and got another cop and sent him to do the job.
Being a cop is important to Jimmy, but so is being a friend. Jimmy found a way to do his duty and still be a good friend. He kept his appointment. He did not betray his friend, at least not to his face.