Split text into phrases of a person and an operator
I think the task you're looking for is called "Punctuation restoration" or "Punctuation prediction". An example of this is described in this paper, or this other paper.
Unfortunately I am not aware of available per-trained model that you might apply to your dataset. Honestly I think that it is unlikely that something trained specifically for costumer service calls exists, unless you want to annotate your own dataset and train a model out of it.