Tell him to find another one that's under the 60K mileage limit and then just pay monthly thereafter which avoids any more hikes - what's the point of a warranty on a used car for a year? it isn't suddenly going to be immune from failures once the year is up.
Tell him to check the reg with the BMW warranty website, he'll then find if they will cover it or not, I've run a few registrations through it and been declined in the past a recent 320d I helped a friend source, we had two nice specced contenders from car supermarkets but BMW refused a warranty quote on both despite being apparently ideal criteria - full BMWSH, under 60K etc - maybe a glitch, but I just moved on to a car that they would cover which they did ironically from a private sale, from a making claim perspective, I'd imagine a full BMWSH makes things easier also.