Here is an A Wright found in National Park Service Soldiers and Sailors in the Cimvil War.

Border's Regiment, Texas Cavalry (Anderson's)Side:ConfederateCompany:H
Soldier's Rank In:Private
Soldier's Rank Out:Private
Alternate name:
Film Number:M227 roll 40Notes:
Plaque Number

You might want to get a copy of his Wife's pension application and see what information is
found in it.