Sir

what you have is probably a chamber for the one of this cartridges: 11,15x52R, 11,15x60R, 11,15x65R

history: .410 ga shotgun brass cases come in use for rifled barrels mayby around 1885( we dont know it exactly). this are allways low power blackpowder rounds chambered most times in Drillings. only the 11,15x65R is in the CIP list with a .445bullet dia. and a max. pressure of 2000 bar. .444 marlin brass is very similar to .410 shotgun brass in diameter, in fact its possible to use the brass in both guns. make a chamber cast and slug the barrel to see what for a case length your gun need. if you have a 60 or 65 mm long chamber try Magtech .410 shotgun brass, its inexpensive and will work with 2000 bar. Maybe you have to trim the rim a lttle bit. The rim of the shotgun case was reworked in old times and you find such cases in old catalogs marked with "LK" for Lancester Kugel---Lancester Bullet.
All center fire shotgun ammo was named lancester cartridge in differenc to lefaucheux pinfire cartridges you find together in ammunitions catalogs in this time.
Shotgun case based bullet cartridges are Lancester Kugelpatronen. German- Austrian full rifled shotgun cartridges are not the same as british paradox or full rifled cartridges.
Max. rim dia. for the LK cartridges is 13,15mm and max. rim thickness is 1,40mm, make a test with .410 ga Magtech brass if it fit the chamber.

greetings from krautland