The Model 1903A3 rifle is base upon the Mauser 98 action but they are not exactly the same.
I checked www.oldguns.net and they show the manufacture date of Remington 1903A3 serial no. 3851292 as 1942.
With the serial number that you have supplied,your Smith-corona model 1903A3 was made in the year 1943.these rifles were only made in the years 1943-1944.If your rifle has a letter C prefix to the serial number,then this indicates that remington also made a model 1903A3 with the same serial number. These were the only 2 manufactures of the 1903A3 rifles.
February 1943
made 1942
August 1943
September 1943
August 1943
July 1943
1944
I don't believe so
It was made in February of 1943.