As the land diameter of the barrels was still given with the gauge number (lead balls to the pound) 62.78 = .420 - .429”, the rifle was made and originally proofed by the Suhl proofhouse between 1893 and 1911. It had both barrels proofed for a 11 mm x60R bp cartridge, either the 11.15x60R Mauser M71 bottlenecked case or the straight taper 11x60R LK “Drillingspatrone”. In the late 1920s the left barrel was relinered in Suhl and duly reproofed for the 5.6x35R Vierling, crown/I = Instandsetzung = repair proofmark. Post-WW2 the rifle was refurbished and restocked, probably in America.
The German 5.6x35R Vierling case was the same as he old blackpowder .22 Winchester Center Fire case, but loaded with smokeless to almost .22 Hornet ballistics. But when Winchester introduced the Hornet as a factory load, they gave the case a thicker rim and a slightly different shoulder to prevent the Hornet loads being chambered in their old weak action blackpowder rifles. Some “generous” Vierling chambers will take some European Hornet brands as is. Many other vierling chambers were rechambered slightly to accept Hornet factory loads. Otherwise you will have to reduce rim thickness of Hornet cases and resize them in custom 5.6x35R Vierling dies.