Actually this is the 1st I have seen a counterstamped (Chinese) counterfeit coin for sale! I sent a note to an established internet seller that he had 2 fake "1805" half cents listed, with one being the counter-stamped version. I explained the issues (1804 C-6 reverse for one) and he asked me to look at another half cent (1804) he was going to list and it was from the same family of fakes. He was grateful for my time and saved him from some "embarrassment" and he decided to send the cs one to me for my collection after ending both auctions. My Coin Week article can be viewed at: https://coinweek.com/counterfeits/struck-counterfeit-coins-a-family-of-struck-fake-half-cents/
Nice. Even nicer that the seller was honest enough to listen and learn, and then reward you for the information. Kind of rare these days.
Stole the photo from face book just to share here. A fairly high grade example of a fake from these dies, without the counter stamp. Barry Murphy