I think kids under 13 using FB put the rest of us in a bad position. It's not fair to the rest of the user community, and frankly, it makes me very uncomfortable.
There are many good reasons for the rule, and I can understand reporting violators.
Asking what do you gain is ironic, on a forum that is largely moderated based on users reporting rule violations.
But regarding your question about telling his mother, I think you have to figure out what message you want to send to your son and what either action will imply:
It's hard to say what he will take away from you saying something or saying nothing.
It could be "My mother won't condone my friends deceiving their parents"
or "I can tell my mom anything and she won't react"
Also, consider what you would want to happen if you were in the other parent's shoes.
Whatever you do, I think you should talk at length with your son about this issue, but not necessarily tell him what you decide to do. Because if you do tell the mom, I don't think your son needs to know or feel guilty about sharing this info with you.