I tried to create this 3d model with a rigging , but when I moved the rigging in a pose the lips would stay in position and stretch.
I means you have vertexes without any weight on them. Do some weight painting. Or, just assign those vertexes to a vertex group.
I, there are some vertex in the back of the lips. I use multiple polygons and join them together. I know the lips at the front, but the back isn’t.