Flo,

According to Sifakis' " Compendium of the Confederate Armies : Texas" , Company H was organized on April 3, 1862 . Their first Commanding Officer was Capt. Thomas J. Catching . They were surrendered by Gen E. Kirby Smith on May 26, 1865. They are listed as participating in the Battle of Galveston Island , January 1, 1863.
Brig Gen Wright/ Col Simpson say this about the regiment in their " Texas in the war, 1861-1865",
The 1st Texas Heavy Artillery Regiment was a 10 battery regiment that was organized in early 1862 at Galveston. This regiment manned the permanent defenses along the upper Texas coast from Sabine Pass to Velasco, with most of it's strength being concentrated at Galveston. It played an important part in the recapture of Galveston on January 1, 1863. Company F ( Davis Guards) was probably most famous company of the regiment since they were commanded by Dick Dowling at Battle of Sabine Pass.
Officers besides Capt Catching were Lts. Everett Lewis, Benjamin Shippand Second Lt John L. Harper, all appointed on April 3, 1862.