Not sure what you mean by stone part and coated part? Do you mean part of it is stone and part coated or is it different types of Formica?
Looking at the complex pattern, I would say your chances of a successful repair are about nil.
Personally, if it bothers you, I would find some new Formica or similar and recover the lot.
If you are determined to repair it, you might have to open out the crack then use an epoxy filler. But the worst bit will be matching colours with say enamel paints. The other alternative if it is valuable to you, is to get it professionally repaired. Given the nature of the Formica surface, glossy etc., I reckon you will not get a repair that doesn't show.
Best bet, get some new Formica, a contact adhesive like EvoStick, overlay it, then get or borrow a laminate trimmer for a professional finish