Latimer Reed has as a family heirloom a piece of rock which may actually have been chipped off the Kaaba by an ancestor, but probably wasn’t. He recounts to the Black Widowers how once, years earlier, someone had tried most desperately to buy it from him, and Henry is able to divine how that was used as a ploy to cover a most clever theft.
This is actually a very nice story, with a clever mystery that has a reasonable and unexpected ending. There are better Black Widower stories than this, but it is definitely one of the good ones.