[morzh]

The magnet can be possibly recharged by locating the poles (likely left and right of that notch where there is no wax) and, using a small strong rod magnet rubbing it, each pole with a different end of the rod magnet.

I do not know if the polarity matters, likely yes, so you could try to determine the polarity of the original with a compass, and them magnetize it the way so it would still attract the same pole of the compass.