Ground is ground. If it's from the engine, find a convenient place on the frame, or metal body of the car and refasten it. If it's from the frame, bolt it to the engine side of the nearest motor mount, or a mounting bolt on any compressor, or alternator-to-block bolt. The latter is the issue in your case.
By the obvious 'shinier' appearance at the end in the pics, that looks like it pulled out of a crimp-on eyelet, which will still be under the original bolt it was attached to.
By the obvious 'shinier' appearance at the end in the pics, that looks like it pulled out of a crimp-on eyelet, which will still be under the original bolt it was attached to.