From the looks....I'm NOT a plumber, But play one at home, The faucet extension is Soldered in & they didn't use the 1/2" NPT connection.
One solution is to cut the faucet off at the extension & Sweat on a 1/2" Female Copper Solder x 1/2" Female NPT Adaptor, Least you won't need to Sweat a connection next time.