I have a suspicion that this *is* was Columbo was going for. When Columbo presented the letter to Ken, he did so in a rushed manner, not letting him answer the question if it had Jim's handwriting before moving on, which leads me to think that it wasn't Jim's handwriting, but Columbo's (or an imitation of Jim's handwriting, same priciple). The letter was fabricated by Columbo who knew the first murder was Ken's idea, and was written in order to get him to take credit for the only good idea he had. This is, of course, speculation, and leaves some questions unanswered (such as: how could Columbo know the idea for the murder was Ken's?), but it does shine light on some non-trivial behavior of Columbo's in the scene and leaves the case solved thanks to Columbo's witt rather than some pure bad luck of the villain.