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The FSR is roughly the equivalent of the National Rifle Association (NRA) in the United States or the DCRA here in Canada.
After losing a War to Russia in 1809, there was a great interest in Shooting and Defence by the Swedish people. Many Rifle and Gun Clubs were then formed. In 1893 the Centralstyrelsen was formed as a Board to regulate National and Regional shooting. This became the Skytteforbundens Overstyrelse more commonly known as the Skytte OS in 1903 (The Shooters Association Supreme Board)
In 1966 this name was changed to Frigvillga Skytterorelsen or FSR. (Volunteer Shooters Association) It seems in Sweden that these rifles, even though they are included in the earlier Skytte OS period, are refered to as FSR rifles as the names are used interchangeably.
What you did not mention in your first post is the holes drilled and tapped into the receiver for the Diopter rear sights. That really clinches it for identification for a FSR range rifle. After WWII, Diopter sights were approved for competition, and there were several types. If the holes are straight across, that is for the Faldt sight. If there is a slot milled in the receiver and two offset holes, that is the GF sight. If the holes are offset, it depends upon the measurements, as it could be a Soderin, Pramm, Elit. Other common sights were the Hooka, Busk, Lyman 48(M), and Hauges.
Many of these rifles were Civilian purchases, and a lot were on loan to the Gun Clubs from the Army. As such, they were sold or loaned with a stipulation that the Government could buy them back in case of an Emergency. Another stipulation was that the rifle could not be "harmed" but could be easily returned to military standards. The two small holes for the Diopter sights was not considered harmful to the operation of the rifle and target sights could be removed with a screwdriver. However, you could not "Bubba" the rifle by "sporterizing" it or cutting it up.
I would suspect that the scope mounting was done after 1980 when the Swedish Military changed from the Mauser System bolt action rifle and sold off a lot of their obsolete firearms. It would appear that someone has also drilled and tapped the side of the receiver for a side mounted scope base. This might be a bit of a challenge to find one that would fit, as these bases were mostly individually mounted and fitted.
Even in the m/41 Sniper rifles, the hole spacing and locations can vary a bit. Many of the mounts were made slightly oversized and filed to fit the individual rifle or base, then numbered to each other.
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