Yosemite won't prompt for 2 factor Auth code

I am not a macOS user but am trying to help my nephew. On his 2014 Mac (running Yosemite, fully updated), he cannot connect to any sites requiring an Apple ID. When he tries to, he's asked for his Apple ID and password. He enters the password on the Mac and his phone prompts with a Deny/Allow access prompt; he hits Allow and is given a two-factor Auth code. The problem is the Mac never prompts for the two-factor Auth code sent to his phone.