I suspect that it was a nickname, rather than them being used as actual sharpshooters. The 40th was nicknamed the "Alabama Sharpshooters" while at Vicksburg. It would seem that this was just Stone's group of Alabama Sharpshooters, with the rest of the Alabama Sharpshooters in parole camp at Demopolis.

I don't know where I got this bit of information, but I have that the companies which later called "Stone's Alabama Sharpshooter Battalion" were not at Vicksburg at the fall because they had been sent to Fort Pemberton.