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Does it have a safety locking lug at the rear of the bolt?
The early Finnbear's with a third locking lug were an exceptionally smooth action. When they did away with the third lug, the overall smoothness took a dive.
Yes, from the information that you have provided, your rifle is a Finnbear.
The Sako A-III is a slightly modified L61R (long) action (the modification is that the bolt has a shroud). The A-III was introduced by Sako in the early 1980s but shortly thereafter was changed to the A-V (which had a slightly longer action tang). All of the L61R / A-III / A-V series are called Finnbears. But not all have the bear's head on the bottom of the pistol grip. By far, the most common chambering is .30-06
The serial number [and manufacturing date] of the first A-III is 530538 [06/03/1978]. So since your rifle's serial number is only slightly larger, we can estimate that it was manufactured from mid-1978 to early-1979. [Sako made the last A-III on 25/09/1981].