What proof did Jack offer of his origins?

Miss Prism, the governess of Cecily, is asked about the male baby that she lost. As a consequence of that, she tells the true story and she apologizes to all of them, because, in a confusion moment, she left the black handbag in Victorian Station with the baby inside. After telling the story, Jack realizes that he also was found in Victorian Station, so he offers the black handbag to Miss Prism like a proof of his origins. Is this the correct answer?