Is it true that a British spy stole a piece of the Black Stone to prove it is not of earthly stones, and it was thus proven to be a unique meteorite?

We have no knowledge of the authenticity of the mentioned story. The confirmation that the Black Stone descended from Paradise is derived from the saying of the Prophet, peace and blessings be upon him, in the hadith (definition) narrated by Ahmad, An-Nasa'i, and At-Tirmidhi: "The Black Stone descended from Paradise, and it was whiter than milk, but the sins of the children of Adam made it black." This hadith was authenticated by At-Tirmidhi, Al-Albani, and Shu'ayb Al-Arna'ut.