A Counterfeit Half Penny, A Freak From The Revolution ?

My grandfather had a coin store in Westchester County, NY, back in the 1960s. I have been going through what remains of his collection and came across this George III half penny. You can see what he thought it was from the packaging in the picture below. My father came along after my grandfather passed and thought it might be counterfeit (that's his handwriting). And now it's my turn. So here it is, weighing in at about 6 grams with a diameter of roughly 26mm, which to my understanding puts this squarely in the counterfeit category. On the other hand, the raised edge and evidence of denticles to the rim (still clearly evident on a small section of the reverse) argues against counterfeit (I think). But something else about it doesn't sit right with me: the legend on the obverse reads GEORGIVS (badly faded) III D G REX, which suggests a later issue coin while the lack of a date and the way the shield leans on the reverse suggests 1st issue. Help!