One or more of Fitzgerald's vouchers show him as commanding a company in Col. Carters Tennessee Volunteers. This would be Carter's 1st Tennessee Cavalry.
I do not find Fitzgerald as being attached to Carter in any document I possess. However, I find it interesting that Carter's Company G which was added at organization was "Formerly Co. 'L', 64th North Carolina Infantry Regiment, Organized September 17, 1862 at Maryville, Blount County, Captains A. P. Wiggins, J. M. Kidd. [Tennesseans in the Civil War, Part 1, "1st (Carter's) Tennessee Cavalry Regiment," p. 50]
Companies 'M' and 'N' must have been blended in somewhere, perhaps with 'L'.
Might take a lot more digging to ferret this out.
You might contact this regimental "expert" found in Carol Botteron's CW Units @ http://sunsite.utk.edu/civil-war/unit5.html This could be an old contact, don't know.
64th NC Infantry dslagle@bellsouth.net (Dan Slagle)
I'll be out in their Greenville area this Memorial Day weekend attending a descendants reunion of the 43rd Tenn.
Good hunting,
George Martin
Sparks, NV