welcome to Blender SE.
First of all i want to say that your question "normally" isn't satisfying enough to really be able to answer your question.
Why not?
Because you wrote just 2 sentences and added 2 pics.
But rigging isn't easy - especially for beginners.
I could now answer also with 1 pic and 1 sentence:
Just parent your upper teeth to your parent upper lip bone and vice versa to your lower lip.

I think this wouldn't be very useful to you because you don't seem to be very familiar with Blender.
But tbh i have no idea how your rigged your mouth or whether you rigged your mouth at all. So now i have to assume a lot of things which you might have been done - or not. And i really like to help people, but often i got then comments "yeah, but i wanted it totally different." or "yeah, but i made it differently". And here begins the frustration of the the ones, who want to help for free in their spare time because they wasted time on answers which aren't very helpful for the one who questions. But the reason is not the answer, but the very short (or bad quality) question which doesn't inform exactly, what is wanted, what is existing and where exactly the problem is. What you want is clear (i think), but you wrote nothing about what you have and how it is made.
Normally those kind of questions will be downvoted (due to lack of information) or ignored (because people who wants to answer make exactly these experiences i just told you).
Well...i try again...for the 1000th time: (of course you are not alone writing such questions)
I assume that you can rig and you have rigged your mouth in maybe a similar way:
So you have some bone for upper and lower lip which can move the lips and you have parented all lower lips to a parent bone (in my case: lower lip) so that you can move the whole lower lip with one bone, as you can see in my gif.

All you have to do now is select all lower teeth...

shift-select your armature, go to pose mode, select your parent lower lip bone...

then press ctrl-P -> Bone.

by this your teeth will move with your lower lip.

And you can still move your lip with your detail bones.
Hope that helps. And i hope your next question here will have more informations so that it is easier to help you. Have a great day!