How does Holmes gets Dr Watson's letters at the stone hut in The Hound of the Baskervilles?
Holmes had his needs provided for by a boy who brought him things from the nearby village, including the forwarded letters from Watson.
When Watson goes to Baskerville Hall to investigate, he believes that Holmes is staying behind in London. He dutifully writes down everything he sees and sends it in letters to Holmes, supposedly in London. Watson is aware of the ancient stone huts that dot the moor countryside, and he hears that someone is staying in one of them, someone who looks like a gentleman.
Apparently not suspicious, Watson continues to send Holmes letters until he literally runs into him in his stone hut. Watson is irritated and hurt, because Holmes kept his presence on the moor a complete secret even from Watson. All of his needs were provided by a boy who brought him food, and apparently the letters, as he hid out in the stone hut. Watson felt that he “deserved better.” He tells him he brought Cartwright from London, the boy who provided his provisions.
Watson first fears that all of his letters (his reports) had been wasted. He learns that is not true.
“Here are your reports, my dear fellow, and very well thumbed, I assure you. I made excellent arrangements, and they are only delayed one day upon their way. I must compliment you exceedingly upon the zeal and the intelligence which you have shown over an extraordinarily difficult case.” (Ch. 12)
Thus Holmes ensured that his secret was kept, and no one knew he was there—not even Watson. This way Watson would not accidentally give anything away in his haste to report to Holmes or ask his advice. Holmes was happy to remain hidden until he was ready to act.