Here is what i have so far. I welcome any additions or corrections....

West's Battery was formed during the spring of 1862 and for a time served in the District of the Indian Territory. It was led by Captain H.C. West.[1][2] The other battery officers were First Lieutenant Dan J. Murphy; Second Lieutenant Benjamin B. Brett; Third Lieutenant John J. Brooks. Lieutenant Brett resigned in the early part of the war, and Lieutenant Brooks succeeded him, the place of the latter being filled by Third Lieutenant Peter Dumas.[3]

Battles
The Desha County Artillery was assigned to Colonel Emmett MacDonald's brigade of Brigadier General John S. Marmaduke's division of Major General Thomas C. Hindman's 1st Corps, Army of the Trans-Mississippi during the Battle of Prairie Grove. At that time the battery consisted of sixty one men, one 6 pound smooth bore cannon, two 12 pound field howitzers.[4] The unit was also present at the battle of Cane Hill, and Van Buren. Capt. Henry Clay West's "Desha County Artillery" was assigned to 2nd Division, 1st Corps, in the Army of the Trans-Mississippi reorganization following the Battle of Prairie Grove.

After Prairie Grove the unit retreated to Van Buren, with the rest of Hindman's Army. The unit spent some time sereving with Confederate forces in Indian Territory (modern day Oklahoma) and thus missed the battle of Helena in July 1863 and the fall of Little Rock in September 1863. In the summer of 1863, the battery was ordered to join Major General Richard Taylor's District of Western Louisiana. West's battery had two 6-pounder smoothbores and two 12-pounder howitzers on February 12, 1864. By the time of the Red River Campaign in the spring of 1864, the unit was assigned to the division artillerry of Brigadier General Jean Jacque Alexandre Alfred Mouton's 2nd Infantry Division of Taylor's command. According to Major Joseph L. Brent's report of the Battle of Mansfield, "Henry C. West's & Moseley's Batteries were in reserve in rear of line of battle & beyond them Farris & Barnes were held ready for any emergency." On April 19, the battery had only three guns--a 6-pounder, a 10-pounder parrott (or 3-inch rifle), and a 12-pounder howitzer. It is unknow what happened to the other 6-pounder and 12-pounder reported in February. The Parrott or 3-inch rifle probably came from the Union cannons captured at Mansfield.[5] The battery then helps harrass the Union fleet as it attempted to escape the falling waters of the Red River. During a five day span in early May, the batteryr helped capture or destroy three transports, two gunboats, and capture numerous prisioners.[6]

In July 1864, following the Red River Campaign, the artillery of the District of Western Louisiana was reorganized and West's battery was assigned to Major G. S. Squires, 2nd Battalion of Colonel Bent's Division Arillery.[7]

On November 19, 1864, General E. Kirby Smith, commanding the Confederate Trans-Mississippi Department, issued Special Orders No. 290, organizing the artillery of the department into battalions. The component batteries rarely, if ever, operated together. They were usually assigned individually to an infantry or cavalry brigade to provide fire support. In this reorganization, West's Battery, armed with 4 guns, and still under the command of Captain Henry Clay West was re-designated as the 4th Arkansas Field Battery and assigned to the 5th Artillery Battalion, commanded by Major William Durbin Blocher.[8]

On December 31, 1864, The battery was assigned to Maj. Thomas A. Faries' 3rd Artillery Battalion, in Maj. Gen. Camille Giles de Polignac's 2nd Infantry Division, in Lieutenant General Simon Bolivar Buckner's First Army Corps.[9]

Lieutenant General Richard Taylor offered Captain West the position of Chief of Artillery with the rank of lieutenant-colonel, but West declined, saying that the people of Desha County had sent him this battery to command and he would "remain with it to the close of the war and take the survivors back to their homes".[10]

Surrender
West's Battery never surrendered. At the end of the war the battery was stationed at Rock Mount, Louisiana, where Captain West disbanded it on May 26, 1865. Twenty six of its men surrendered at Pine Bluff, Arkansas, on May 22, 1865.