This is actually a game fragment, published in the Chess Monthly in 1859 as
"An End-Game by Morphy"
The circumstances of the game were published elsewhere in the periodical:
"We regret to state, that it is very probable that Mr. Morphy will be obliged to relinquish his journey to Berlin. The arrangements connected with the publication of the French and English editions of his games have detained him so long in Paris, that, in order to reach this country in April, he would even be compelled to abridge his contemplated sojourn in England, on his way home. The Duke Decazes had given him a dinner, at which a number of grave senators and warlike generals assembled to do honor to the young hero. Mr. Morphy, at the request of the company, played two simultaneous blindfold games and took part, at the same time, in an animated conversation."
The fragment or end-game proceeds from White's 20th move: