Personally I would retopologise the head and model a mouth bag where the lips intersect, then bring it back into ZB and project all, that way you're not destroying the sculpt. The mouth would look open but you could close it easily with topological masking.
You most likely gonna lose those ppaint and some sculpting details, so definitely duplicate first. Mask off the whole dog, except his lower jaws, then rotate it down to open his mouth. You will probably need to dynamesh/zremesher to re-distribute his poly. Then pulls his inner mouth back to make his throat or something. It…