Despite the name, the Moscow mule was invented in the United States, most likely in 1941. Its creators were businessmen with drinks to sell, and who mixed it first is still argued over.
One of them was John G. Martin, president of G. F. Heublein Brothers of Hartford, Connecticut. Difford's Guide says he had acquired the rights to Smirnoff vodka for Heublein in 1939. The other was John A. "Jack" Morgan, owner of the Cock 'n' Bull restaurant in Hollywood. Morgan was trying to launch his own ginger beer, and sales were not going well.
The usual story is that the two men mixed their products with lime and found a hit. A 1948 New York Herald Tribune account sets the moment in 1941 at the Chatham Hotel in New York. It says the drink was christened the Moscow mule four or five days later. A rival version, in a 2007 Wall Street Journal article by Eric Felten, credits Wes Price, head bartender at the Cock 'n' Bull on the Sunset Strip. Price said, "I just wanted to clean out the basement," meaning the unsold ginger beer.
"Moscow" points at the vodka. For "mule," Merriam-Webster says the drink was probably so called because the vodka gave it a figurative kick, like a mule. The dictionary's earliest record of the name is 1943. The etymology researcher Barry Popik has found it a year earlier, in Town & Country in August 1942. That listing calls it "a realistic tribute to the city's defenders."
Martin then sold the drink bar by bar. He asked bartenders to pose with a copper mug and a bottle of Smirnoff, took Polaroid pictures of them, and showed the photos at the next bar.
The copper mug has more origin stories than the drink. The 1948 account says the partners ordered 500 copper mugs embossed with "Little Moscows." One later story, reported by Thrillist and relayed by Tasting Table, credits Morgan's girlfriend, Ozeline Schmidt. A family member had supposedly willed her a copper mine and a stock of copper products. Another names Sophie Berezinski, a copper factory heiress who brought a cache of copper mugs with her when she emigrated from Russia.
Tasting Table finds both stories unlikely. It favors the cocktail historian George Sinclair, who argued that English-style pubs like the Cock 'n' Bull already had copper mugs for serving beer.