You can inject some 2 part clear epoxy into it, but you were given a "second" with poor quality stone and an even poorer fit for the undermount sink. I know it seems counter intuitive to throw something pretty away, but you'd be better off not putting that into your home. It will eventually crack somewhere else, and the caulk that is the only thing between you and a wet vanity cabinet will degrade and leak at some point. It's a given that you will need to do a monthly inspection on it and keep it up.

If you can't cut it into coasters and salvage the sink for something else, it belongs in the rubbish bin from which it was rescued.