Model A's were available in 22-250 Remington, .270 Winchester, .243 Winchester, .308 Winchester, 30-06 Springfield, 7mm Remington Magnum and 300 Winchester Magnum.
They were made from 1969 to 1972.
If there are no caliber markings on the barrel, the only sure fire way to know what it's chambered for is to do a chamber cast and then measure the "plug" to see what cartridge dimension it matches. It could of had a barrel swap done on it for a custom build, and with no barrel markings, it's anyone's guess.
I figured it out by finding the fact that three calibers (.25-06,.243 and 7mmRem.Mag) came with six lands and grooves where all others had four. My rifling also had 6 lands and grooves. I read up and saw where someone had a 7mmRem.Mag and it was serial numbered 13 rifles before mine. I took these said facts in mind and took a .270 round and inserted it into the muzzle and it went in.This being said, I knew it must be larger than .243. I also did this with a .30-06 round which showed me .30 cal was too large for the bore. so I hand chambered the .270 round lightly to compare and it was loose. Finally I compared the round to the bolt and ejector and it was too small. Knowing that .270 and 7mm are closest in diameter with 7mm having a larger casing I trialed the 7mm in the same manner after buying a box of rounds. I was sure at this point I wouldn't be wasting my money on rounds I had no rifle for... lol. Viola! 7mm Rem.Mag. And with the serial number being as close to the other person's which was manufactured late 1970 to 1971 I took the assumption it was probably correct for my rifle as well.
You can get the exact build date by using the Husquvarna website and the serial number btw. It will also tell you the caliber. I own a very pristine 308. Never fired before I got it. My backup hunting rifle. Put a Timney trigger in it last year. Stock triggers blow.
Mine shoots quarter sized groups at 200 yards with handloaded Bergers in Lapua brass.