Buttons showing a "game" animal are known to collectors as a Sportsman's buttons. They were very popular on hunting-coats in the 1800s.
Need to see a well-focused closeup photo of the (cleaned) back of your boar's-head Sportsman's button to have any hope of time-dating it. Does it have a backmark?
I'll have to check. It's a two piece button. I found a pic of one on the Web. It's in the big book of buttons on page 276. It didn't have any more info than that though.
As CBG stated fairly common in 19th Century sites.It has been told that often times in England Hunting clubs would give out buttons featuring and animal the bearer had taken,like a "score",and he would sew it on his coat?I dont know what truth there is to that?