It looks to me like you need to have the stone lifted, the voids underneath filled, and then the stone reinstalled and properly grouted.

I think you may want to see if you can get a stone mason, familiar with that particular type of stone.

You can patch with epoxy putty, like this:
Atlas Min. & Chem. 530318 Pool Putty White 14 Oz.
but it wouldn't look great, and you might have a hard time getting all the epoxy off, when you did fix it 'right'.