This is apparently a tourmaline set in Sterling from an estate sale. Could this be synthetic tourmaline? Or could it be natural? Seller labelled as from the 1940s...
Tourmaline is cheap but I'd expect if it was a real tourmaline unless it wasn't worn much to be showing more signs of wear than that. Set in silver my guess would be synthetic green beryl or the slightly rarer synthetic green spinel which can also test positive as tourmaline.
Take it to a jeweller or a gemstone dealer and ask them to tell you, without seeing it in person I can't tell for sure, it looks like a synthetic stone but I could be wrong.