Sherlock Holmes - A Case of Identity (ASH)

Mary Sutherland seeks Sherlock Holmes and Dr. Watson's help when her fiancé, Hosmer Angel, disappears on their wedding day. Holmes discovers that Sutherland knew little about Angel, who was a reserved Londoner that communicated with her through typewritten letters and met her only when her disapproving stepfather, James Windibank, claimed to be away on business.
Holmes deduces that Windibank and Angel are the same person, using Sutherland's inheritance to support his lifestyle. Windibank posed as Angel before orchestrating his disappearance to continue his scheme. Despite solving the mystery, Holmes chooses not to share his findings with Sutherland, advising her to move on from Angel. She refuses, holding out hope for his return. Holmes predicts that Windibank will continue his criminal activities until he is apprehended and punished.

Story from Arthur Conan Doyle - The Adventures of Sherlock Holmes in 1891.