During my years working in the foster program of a large, regional animal shelter I saw a lot of dogs come in as strays after being hit by a car, then needing foster placement after having a leg amputated because of the injury.
They all did fantastically well. As others have mentioned, they don't spend time mourning the four legs they use to have, or what others might think of them, or what they can't do anymore. They just don't look at the world or their lives in those terms. If anything, having a constant source of pain gone appears to make them very frisky and happy. They heal so quickly, it is really amazing.
They adjust physically very, very well. The one leg left on whichever end seems to naturally accommodate, and adjusts balance needs by taking what looks like a more centered position underneath the body. This tripod stance is very steady and balanced and they can do everything a four-legged dog can do (run up and down stairs, jump on and off furniture, etc.), not to mention giving them the name that most vets use to describe them after the amputation (they really are called "tripods").
I hope your BF comes around and realizes that the amputation will not be a big deal at all for your dog. I wish you all good luck!