However, I would check the 9th Louisiana Infantry rosters since a company of 1861 volunteers from Jackson Parish enrolled in the 9th Louisiana Infantry was transferred to the 12th Louisiana Infantry in Mississippi. This involved a prisoner exchange in September 1862 and I won't go into that detail here. Those men who did not go home on furlough from Virginia in February 1862 were allowed to transfer to the 12th Louisiana in Mississippi. Some chose not to do so and transferred to other companies in the 9th Louisiana Infantry and remained in Virginia. I have found at least one soldier's headstone in Virginia attributed to one of the 9th/12th Louisiana soldiers. I don't think it was this guy, but I am away from my hard copy archives at the moment and don't remember the name. His grave was in the Valley, not near Richmond.
Ken's point is on the mark. POWs from the 12th Louisiana captured in Mississippi and Georgia trickled through Richmond in the spring of 1865 as part of the "humanitarian releases" in February and March 1865.
You might also want to check the CMSR for the 12th Louisiaha Heavy Artillery regiment which had men captured at Port Hudson, and Vicksburg if I remember rightly, and sent north to POW camps. The 12th Battalion, Louisiana Infantry had nothing to do with either the infantry or artillery regiments. It was merged with the 11th Battalion and the 24th (the Crescent) Louisiana Infantry regiment into the Consoldiated Crescent. I have not encounted any POW reoords of men from the 12th Battalion or Consolidated Crescent being sent north and east. But I have learned to "never say never" in this Civil War research business.
Hugh