Since you know these people better than I ever will, it will just come down to what these people are like; does your bf sound like the type of person to steal money or does your mate sound like the type of person to try and create drama with your bf.
If its a situation that isnt able to die down, then youre going to have think about getting rid of one of them. I've seen people who have friends that try to ruin others relationships, because it would damage the friendship. Alternatively, it might just end up being a case of your mate thinking of the wrong person.
The fact that youve lived with your bf for 3 years and you havent seen him do anything like what your mate is suggesting means that your bf is more likely to be innocent, since living with someone is the most effective way to see what someone is truly like.