I love how people who are all pro-vax think that the unvaxed are some huge risk to them. It is like you can be perfectly immune but as soon as you come into contact with someone who isn't vaxed it all wears off or something. Like kryptonite.
I would think that, in theory, it is possible to get mumps from the vax. I also think that, in theory, it would be possible to get it from someone who was recently vaxed. But both of those situations would have to happen within a few weeks of receiving the vax. How old is the child in question?
What is more likely is that a) the vaccine didn't work in his case, and b) he picked it up from someone who also didn't seroconvert or whose immunity had warn off. That is the other issue.... nobody knows how long these things last. Ask your friend if SHE is up to date on her vax?