Armature doesn't work on a part of my mesh

So I created a model and I’ve made a mouth. When I wanted to parent it with the armature with automatic weight , as you can see, and then I move a bone, only one part of the mouth moves with it.
Ps: the mouth is divided into two parts but they’re both in the same mesh

I’ve already checked the vertex groups.

Have a good day,thanks.

Post your blend to let people fix your problem. Happy holidays!

Thanks for your answer.
Finally the problem has been fixed. I just had to add a bone