I recently came across a reference to a (purported) letter from Olga To British author John Buchan. The reference appeared in a book not otherwise dealing with either one. Buchan was a pro-British imperialist writer and journalist popular in the early twentieth century . He wrote what you might call patriotic(to Great Britain) spy and adventure thrillers that celebrated the feats of some daring young fellow who would thwart some (often foreign) threat to good old British values. He wrote The Thirty-nine Steps[/i [/ , a big hit as both a book and movie.
At any rate, the book I was reading claimed that Olga wrote him a fan letter from Tobolsk, saying that she'd enjoyed his latest story, as did her sisters, and father. No source was provided for this reference and some of the footnotes in the book were unreliable so I'm doubtful that Olga wrote such a letter. Not to mention that it seems farfetched to think of Imperial Family letters being allowed to be mailed to Great Britain.
On the other hand , totally making up a story about a Russian Grand Duchess writing to a British author seems unlikely too. And, we know that Nicholas and the Gds liked to read popular fiction of the day , for example, Mlllionaire Girl.
So, such a letter seems intriguing, but presently very much 'unconfirmed.'