The Eagle N (Nazi style) was, as RJay says, the regular commercial Nitro proof; it does not indicate military or government ownership. Many "bringback" guns were taken from civilians, not from government officials or German military personnel.
When the Allies invaded Germany, they placed an immediate ban on civilian possession of firearms. While enforcement was spotty, many Germans simply turned their privately-owned guns over to Allied soldiers. When the Allies did enforce the rules, they usually destroyed the guns by laying them on the street and running a tank over them. Many fine hunting rifles, shotguns and multi-barrel sporting arms were destroyed that way.
We should bear that kind of thing in mind when a politician says he doesn't want to confiscate and destroy "sporting" guns, only "evil" military-type guns. (Note: All bolt action rifles are "military type" guns, and even lever actions have been used by armies. So that category of "war weapons that have no place in civilian life" may be a lot broader than the politicians want us to think.)
Jim
Jim