Kindly provide some details regarding the plot of science fiction 'A Borrowed Man' from the given passage.

1. In the 22nd century, Ern A. Smithe is a "reclone" of a mystery writer, embedded with the recorded memories of his original and stored in a library where patrons can consult or borrow him.
2. He is checked out by a woman who hopes that he can help solve the deaths of her father and brother, because her father's safe had contained nothing except one of Smithe's novels.
3.  However, Smithe's original was not a detective, only someone who wrote about them — and his knowledge of the world is over a century out of date.