According to the information I found at the Confederate Research Center at Hill College, the the following is the history of the 1st Texas Cavalry near the end of the war:
On April 18,1864, Major Michael Looscan is placed in command of the 1st Texas Cavalry Regiment at the battle of Poison Springs, Arkansas.
In July 1864, Col Peter C.Hardeman reassumes command of the 1st Texas Cavalry Regiment
In September 1864 Col.Hardeman's 1st Texas Cavalry is assigned to Brig. Gen. Richard M. Gano's 5th Texas Cavalry Brigade and participates in the second battle of Cabin Creek,I.T. which occurred at 2 AM on September 19,1864 which was the last action in Indian Territory. Gano's Brigade consisted of Col.Charles DeMorse's 29th Texas Cavalry; Col. Edward Gurley's 30th texas Cavalry; Col James Duff's 33rd Texas Cavalry; Col.Leonidias Martin's 5th Texas Partisan Rangers; Lt. Col. Chaplin Good's Battalion, and Lt.Col. John W.Well's Battalion.
In late September, 1864, Col. Hardeman and the 1st Texas Cavalry returned to Fannin County to regain regimental troop stength.
In October, 1864, the 1st Texas Cavalry was still in Brig. Gen.Richard M.Gano's 5th Texas Cavalry Brigade, Maj.Gen. Samuel B.Maxey's 2nd Texas Cavalry Division, 1st Corps, Trans-Mississippi Department.
In December 1864, Capt. Jackson M. McFarland's and Capt. John W. Bone's independent spy companies in Grayson and Fannin Counties, previously attached to Col.James C. Bourland's Border Regiment are reassigned to Col. Hardeman's 1st Texas Cavalry Regiment. This transfer of troops was done at the request of Col. Hardeman in order to bring his command to regimental strength.
In January 1865, the 1st (4th) Cavalry Battalion, of the former Arizona Brigade, is consolidated with Col. Peter Hardeman's 1st Texas Cavalry Regiment to form a brigade. The brigade is ordered to report to Maj. Gen. John A. Wharton at Hempstead, Texas where they are to be dismounted and are to be assigned to Harrisburg (Houston) for coastal defense.
In March 1865, Col. Peter C.Hardeman resigns and the 1st Texas Cavalry Regiment is dismounted at Hempstead, Texas.
In April, 1865, Col. Peter C. Hardeman takes his family to Matamoros, Mexico and departs with a saw mill to Sao Paulo Brazil where he establishes the American Colony of Cillo, near Americana and never returns. His descendants still live in Brazil today.
On May 26, 1865, the Trans-Mississippi Department is surrendered by Gen. Edmund Kirby-Smith.
From what I determined, Col. Peter C.Hardeman's 1st Texas Cavalry and Col.Trezevant C.Hawpe's 31st Texas Cavalry were never consolidated into one unit. The temporary transfer of command from the 1st to the 31st Texas Cavalry Regiments by Maj. Michael Looscan in April 1864 has contributed to the confusion of the two regiments until July 1864, when Col. Hardeman reassumed command of the 1st Texas Cavalry, the regiment was placed in Brig.Gen. Richard M. Gano's Brigade and the the 31st Texas Cavalry was placed in Poliganac's Brigade.