I think I would say that the climax of the story is when the police officer (not Jimmy Wells, but the second one who comes to arrest Bob) tells Bob that he is under arrest.
I think I would say that because a story is supposed to have some falling action after the climax, so if the letter is it, then there is no falling action.
In addition, finding out that Bob is under arrest and that the second policeman is not really Jimmy Wells is probably the most tense moment. By contrast, the letter is just explaining what has happened and why. It's more of a "cleaning up" thing that explains what's happened, and that is what falling action is supposed to do.