Here's why it's tricky:
* Canon vs. Adaptations: The original Sherlock Holmes stories by Sir Arthur Conan Doyle don't explicitly state a specific date. They mention the address, but not a moving-in date. Many adaptations (movies, TV shows) have their own interpretations of this.
* "The Adventure of the Speckled Band" is the first story to mention 221B Baker Street. But the narrative implies that Watson is already living there, with Sherlock joining him later.
* "A Scandal in Bohemia" suggests a longer residency, as Sherlock describes the address with familiarity, but again, no precise date is given.
In conclusion: It's more accurate to say that Sherlock Holmes lived at 221B Baker Street during the period of the original Sherlock Holmes stories, but a specific moving-in date is not provided by the canon.