The 13th Louisiana underwent massive changes through the war and it was VERY common for the men of this regiment to have been shuffled. For example, when the 11th Louisiana and 21st Louisiana regiments were disbanded their men were distributed to all the Louisiana regiments in Adams' Brigade (13th, 16th, 20th, 25th and Austin's Bn); with half of the 11th La going to the 13th La. By November 1862 the 13th and 20th Louisiana were merged (each regiment actually condensing themselves to properly fill 10 full companies between the two regiments). Take into account the 20th La underwent several changes replacing two displaced companies and men from the 11th, 13th, 20th and 21st Regiments all transferred over to fill the vacancies. More than likely the reference to him being in Company H was a typ but could have been a possibility.
Michael McGrath actually began his service in Company C. I have been trying to make sense of the 20th Regiment's roster for sometime and organize it and it overlaps with the 13th La several times. I was guess at this point he was transferred to Co. K in the consolidation of the two regiments (13th and 20th) in Nov. 62. In the new 13th & 20th Louisiana the 13th La was condensed into five companies to be the new Companies B,C,E,I and K. The 20th Louisiana was condensed to form Companies A,D,F,G and H.
Now that you are TOTALLY confused with all this mess the units were organized into different consolidations during the Spanish Fort siege. During this campaign the regiment was merged with the 4th La, 30th La and Austins Bn. Right now, no information how they were divided up into companies, IF they were.
After the fall of Mobile the Louisiana regiments were again consolidated into two regiments: The Pelican and Chalmette Regiments. The 13th Louisiana was merged into the Chalmette Regiment of which Company H was made up of the 14th La. Bn.
Phew...hope this helped a little.