Here's how he does it:
1. Observing Details: Holmes meticulously observes Mary Sutherland, noticing her clothes, her mannerisms, and her reactions to questions. He notices discrepancies in her story, like the inconsistency of her fiance's handwriting and the lack of any concrete details about his life.
2. Deduction and Inference: Based on his observations, Holmes deduces that Mary's fiance is not a real person but rather a fabricated identity created by someone else. He uses his knowledge of human behavior and his ability to connect seemingly unrelated facts to reach this conclusion.
3. Investigating the Past: Holmes digs into Mary's past, finding clues about her relationship with a former suitor named "Honoria" and a possible motive for someone to want to keep her from marrying.
4. Uncovering the Truth: Holmes discovers that Mary's "fiance" is actually her former suitor, who is now a woman pretending to be a man. She is trying to keep Mary from marrying another man because she still loves her.
5. The Revelation: Holmes reveals the truth to Mary, breaking her heart but freeing her from the deception. He helps her understand that she was being manipulated and encourages her to move on.
Essentially, Holmes solves the mystery by using his sharp observation skills, deductive reasoning, and knowledge of human nature to uncover the hidden truth behind a fabricated identity. His solution is not just about finding a missing person but about revealing the underlying motivations and emotions driving the deception.