What clues did Sherlock Holmes work upon to get at the fact that the story of the three Garridebs was a ruse?

The first time Holmes felt wry of the story when the American Garrideb was angry at Nathan to have involved a detective. When Sherlock noticed the Garrideb in English appearance and he pointed it out to him that how come that he was an American and yet was dressed so English. The American said that he was a lawyer in Kansas, Holmes made his bait by pointing out to a unreal late Dr. Lysander Starr, who Holmes said to be a Mayor in 1830. and as he had suspected, Garrideb fell for it, he reciprocated by saying that good old Dr. Starr's name was still honoured. Holmes was then sure that as he had suspected, Garrideb was never a lawyer in Kansas. Holmes grew sure of that the story of Alexander Garrideb was made up by John Garrideb when he brought an advertisement published in a local paper of Birmingham that was from some Howard Garrideb. Holmes and Watson both noticed the written piece to have been in American English and they concluded that the piece was published in the paper by Garrideb himself to set Nathan off to Birmingham to buy time so he can intrude in his room without any disturbance.