I'm going to make a mom joke about my friend's dead mother
That seems like it would be in bad taste. Why would you joke about your friend's dead mom?
Yes, this is how I bring fun to my friend's life.
Was she really old? If she was young and it was unexpected, you might want to think twice about that. Maybe he would find it funny -- you know him so you should know how he'll respond.
She was very old, 80.
Even if she was older, the loss of a parent can be devastating. Personally I would hold off on making any jokes and allow my friend to grieve. However you know your friend, but I would still think carefully about how you would approach them during this difficult time.