What muscle forms the labia of the mouth and controls most lip movement, including puckering?

Orbicularis oris    

The orbicularis oris muscle is positioned surrounding the mouth and within the labia. It acts to control the movement of the lips.

Orbicularis Oris is the muscle that forms in the labia of the mouth. It surrounds the mouth and this muscle inserts directly on the lips. Most often, it is called as "the kissing muscle", according to an article in Healthline.