The most important theme is honor represented in different ways:
A) Bob honored Jim's friendship by traveling "thousands of miles" to be there, and claims it to be worth it if his friend will be there.
B) Jim honored his duty as a policeman by declaring his intention of arresting Bob, since he was a most-wanted man.
C) Jim also honored their friendship by asking another policeman to do the deeds, after all, they did share a piece of their lifetimes, and he honored that.
I think it could be argued that the theme of "After Twenty Years" is a simple and familiar one: "Crime does not pay." The character who is most affected by the events in the story is the man called "Silky" Bob. (His last name is not given, possibly because he has changed his last name so many times over twenty years that nobody knows what his real name is.) As far as Jimmy Wells is concerned, he only appears at the beginning of the story and then vanishes into the night. And even then he is not identified to Bob or to the reader. He is just another uniformed policeman walking his beat. At the end Jimmy is only represented by a note to Bob. Jimmy himself never reappears. So it is Bob's story, and therefore the theme must apply to Bob.
"Silky" Bob has obviously been pursuing a criminal career. He is a materialist, a hedonist, and an exhibitionist. He wants to get a lot of money and spend it on luxuries, including diamonds and expensive cigars. His life of crime has forced him to keep on the move, one step ahead of the law and one step ahead of the people he has exploited. As a result he has never had a home or a family or any friends. "A rolling stone gathers no moss." And in the end he is taken off to prison, where he may be incarcerated for many years. He may have been in prisons before. Superficially he is successful, but in reality his life has been wasted and he ends up a failure.
In contrast, Jimmy has followed a straight and narrow path all his life. He is not wealthy, but he is secure and respected. He probably has a wife, a home, and a family. The contrast between the careers of these two friends seems intended to illustrate the old truth that crime does not pay. It is an intentional irony that the young man who turns into a crook is turned over to the law by the young man who turns into a cop. This would never have happened if they hadn't made a date to meet each other after twenty years on the spot where the story takes place.
The story is appealing partly because of its strange premise--that two young men could make an agreement to meet each other again after twenty years and that they should actually remember the agreement and keep the appointment at almost exactly ten o'clock on the appointed night. "After Twenty Years" is vaguely similar to Anton Chekhov's story "The Bet," because two men also make a preposterous agreement. One of them will remain the other's prisoner for fifteen years and will receive two million rubles if he can manage to endure solitary confinement for that length of time. Such a bet is just barely believable, just as the agreement between Bob and Jimmy is just barely believable, because of the great length of time involved. How can anyone plan that far ahead?
BOTH FRIENDS WERE SINCERE AND BOTH HV A SOFT CORNER FOR EACH OTHER IN THIER HEARTS..THEY DIDN,T WANT TO HURT EACH OTHER..THIS SHOWS THAT INFACT , JIMMY AND BOB MET AFTER LONG TIME BUT THE LOVE BETWEEN THEM WAS NEVRE BECOME LESS FOR EACH OTHER..