I’m using the flexrig and I wanted to add a beard that moves with the lips. I’ve been able to attach the beard so it moves with the head, but I have no idea how to get it set up so it moves when the character’s mouth opens.
This is just general, but...
Find the bones to which the lips are attached and weight-painted.
Attach/weight-paint the beard onto those bones instead of having the entire beard attached to the head bone.