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In 1938, the Swedes recognized the value and need for a shorter rifle. A program was instituted by Carl Gustafs to convert some of the existing m/96 rifles to the m/38 standards. When WWII broke out, the Carl Gustafs State Arsenal concentrated on heavier weapons, such as machine guns, and Husqvarna was asked to continue with the balance of this program, and also make new m/38 rifles. The Swedes considered ALL these rifles as m38 rifles and no distinction was made between them, thus the converted m/96 is a m38 and not a m96/38 or any such designation.
Early conversions had the straight bolt handle, and the proper rear sight is the Vasteraas micrometer adjustable rear sight. After Husqvarna started making the new m/38 rifles, they received permission to use the turned down bolt handle, as they were already set up for it with their sporting rifles. A few very early HVA m/38 rifles did have a straight bolt handle.
Your rifle is part of a 40,000 production of rifles made by Mauser in 1899 and 1900. Serial numbers were in a block from approximately 19,000 to 59,000. This was to keep the Swedish Military rearmament on schedule, as machinery for production by Carl Gustafs was delayed. The A/N after the Mauser name is for the factory at NECKAR.
As far as wood goes, most of the conversions used the original stocks. Wood up to about 1915 was generally Walnut, but due to a scarcity of supply due to WWI, alternates were tried. Most common were Beech, Elm, and Maple, but some Mahogany stocks exist. After about 1919, Beech was the wood of choice for the m/96, and the newly made HVA m/38 rifles. Sometimes Beech replacement stocks are found on a converted rifle, but that was because the original stock was not serviceable.
Not all m38 rifles had turned down bolt handles, and the Infantry generally retained their m/96 rifles while the m/38 were more common issue for secondary troops such as Artillery, and Supply Troops who did not have an urgent front line need for a rifle.
The best reference book for Swedish Mausers is "Crown Jewels." Unfortunately it is out of print and almost anyone who has a copy guards it like the Crown Jewels.