The OP rifle is a very common design. .22rf is common, but 6mmrf and others were made.
Made in pre-WW2 Europe, it was sold under the Anschutz name (I assume they made it) and you see a large number of them with the GECO name on them, German retailer Gustoff Genschow (sp?)
The former are sometimes marked Original Karbiner,,the latter were sold with Model names such as 1919, 1921, ect. Genschow was not a mfg'r, so maybe Anschutz made theirs also.
Old print ads from the era show up with them.
Some were made in Belgium also even with the FN marking on them.
Sort them out by proof marks. The pre-War German will have such as proof marks. Then change to the Nazi era marks as they were made into the early 40's.
Lots of variations in stocks, markings, trigger guards, forend tips or lack or them,,same with butt plates. Sights vary.
The action is pretty much standard with the 1/2 moon extractor doubling as the ejector..
Those Mosin Nagant single shot 22 Training Rifle that were imported a few years back (Polish made?) used the same design in it's action.
I have an Anschutz 22LR plain rifle, stamped steel trigger guard and steel butt plate that my father brought back from German after WW2. It is Eagle/N proofed (nazi era). He said they picked it up out of a pile of guns that were destoyed by running over them with their tanks in a village.
It and a leather bag of .22 ammo survived. He and the crew kept it in their Sherman tank for the entire time they were there.
I have another marked JGA on the recv'r ring. It has a cheek piece stock, double set triggers, horn forend tip, same elevation screw adj rear sight as the above rifle. Was in bad shape,,being put back right just because.
Not worth a whole lot,,they sell for a $100 to $200 depending on the condition and features.
Simpsons in Illinois usually has a page or so of the Geco and Begian made varietys for sale. Once in a while an Anschutz marked rifle.