heres some information from the gotavapen.se website - there are several members here that knows more but your assumption is more or less correct.
"There was a civilian production of the m/96 as well. The rifle organization "Frivilliga skytterörelsen" (FSR) ordered some 20000 m/96 rifles from Husqvarna in the beginning of the 1940s. (1940-1943 circa)
These rifles were made to the same specifications as the armys m/96 rifles and the production was partly financed by the Crown. They were sold to members of the "FSR" at a low cost (200 kronen) on the condition that the owner would sell his rifle back to the Army in case of total mobilization.
About 5000 of the FSR-rifles used a new m/43 leaf sight in 50 m intervals from 100 to 600 metres, and 100 m intervals from 600 to 800 metres. The sight ladder is stamped "1", "2", "3", "4", "5", "6" and "8" on the left side, and with index lines for 50m and a "7" on the right side.
About 12000 of the FSR-rifles used a sight called the AGJ-sight made by "A. G. Johanssons Metallfabrik AB" in Västerås. The AGJ sight is marked "SM sikte agj-ram" and looks very similar to the later "SM sikte m/55" used on the m/41 snipers rifle."
and this one as well
"There was a civilian production of the m/96 as well. The rifle organization "Frivilliga skytterörelsen" (FSR) ordered some 20000 m/96 rifles from Husqvarna in the beginning of the 1940s. (1940-1943 circa)
These rifles were made to the same specifications as the armys m/96 rifles and the production was partly financed by the Crown. They were sold to members of the "FSR" at a low cost (200 kronen) on the condition that the owner would sell his rifle back to the Army in case of total mobilization.
About 5000 of the FSR-rifles used a new m/43 leaf sight in 50 m intervals from 100 to 600 metres, and 100 m intervals from 600 to 800 metres. The sight ladder is stamped "1", "2", "3", "4", "5", "6" and "8" on the left side, and with index lines for 50m and a "7" on the right side.
About 12000 of the FSR-rifles used a sight called the AGJ-sight made by "A. G. Johanssons Metallfabrik AB" in Västerås. The AGJ sight is marked "SM sikte agj-ram" and looks very similar to the later "SM sikte m/55" used on the m/41 snipers rifle."
and this one as well