Peter Ravn Lund’s book on Christoph Funk is also available through the German Gun Collectors Association, https://www.germanguns.com/shop/books/page/2/
Your rifle was proofed January 1940. Funk built it on s WW1 Karabiner 98 AZ small ring Mauser action. The barrel was supplied by the Suhl barrelmaker Louis Kelber. The 1970s scope was mounted much later.
The rifle was retailed by Rudolf Zimmermann, Koenigsberg in East Prussia, now Kaliningrad, Russia since 1945.
The 5.6x61 Super Express vom Hofe cartridge was introduced by the ballistic experimenter Ernst August vom Hofe, Berlin in 1937. Nearly all prewar "vom Hofe" rifles were built by Ch.Funk.
5.6x61 ammo is a real problem. This proprietary cartridge was once distributed by v.Hofe’s successor, Gehmann in Karlsruhe https://gehmann.com/english/impressum.php . But their webpage does not show it anymore. Handloading is a problem too. The case is based as a necked down 6.5x61, an experimental cartridge once made by DWM for Sweden. So it has the .10” larger base diameter of the 6.5x55 SE. This makes reforming available brass near impossible. Here in Germany old “Gehmann” or Horneber brass is available sometimes. Or you may ask https://huelsenmanufaktur.de/homepage/ .
The 5.6x61 used 77 gr .228” bullets. The 70 gr .228 bullets still made for the 5.6x52R aka .22 HP Savage are too fragile for the v.Hofe. Perhaps DKT or Hawk can supply strong jacket 77gr bullets in this odd diameter?
The DEVA once listed two pressure tested loads:
70 gr Hornady, 51.5 gr IMR 4831 for 3540 fps
77 gr Gehmann original, 53.2 gr IMR 4831 for 3500 fps
As the cartridge is known for Secondary Explosion Effects, downloading is advised against.