Weird. Made in the 1800s, I have to wonder if it was sold in earnest, or if it was some kind of collectable, like we have with lightsabres and the like today.
I’m not saying this is the case with your particular item, but I know of artists who do pieces like this. They are painstakingly crafted and sometimes have actual antiques. I’ve seen them sold on eBay. “Authentic” might be meant to be taken with a big grain of salt…(especially since vampires aren’t, y’know, real ;)).
I’m betting it’s a fake. The silver bullet thing, to my knowledge, didn’t show up until werewolf movies in the 20th century.
EDIT: Fake in the sense that this wasn’t originally a vampire killing kit, that is. The individual pieces may well be authentic.
Here’s some research into the matter.