Let's try this again, from the top:

Forrest’s Cavalry Battalion formed about October 16, 1861, at Memphis, Tennessee under Nathan B. Forrest, Lt. Col., and David C. Kelley, Major:

Company “A” of Meade and Breckinridge Counties, Kentucky “Boone Rangers”
Company “B” of Wilcox and Monroe Counties “Pope Walker Rangers”
Company “C” of Shelby County, Tennessee “Forrest Rangers”
Company “D” of Red River County, Texas
Company “E” of Cherokee County
Company “F” of Madison County “Kelley Troopers”
Company “G” of Mercer County, Kentucky “Kentucky Rebels”
Company “H” of Marshall County “Russell Rangers”

By early February of 1862 two other companies had joined the battalion:

Company “I” of Madison County “North Alabama Rangers”
Company “K” of Shelby County, Tennessee “McDonald Dragoons”

Forrest’s regiment organized at Burnsville MS on Apr. 3, 1862. Gould’s and Davis’s companies surrendered at Fort Donelson, Tennessee, and were replaced by others. After Forrest was wounded at Monterey TN, the four Alabama companies began operating as a separate battalion under Captain W. C. Bacot.

Russell's 4th Alabama Cavalry probably organized at Columbia, Tennessee, November 23, 1862. It including four companies from Forrest’s Tennessee Cavalry Regiment and five companies from Russell's 15th Tennessee Partisan Ranger Battalion. The tenth company was an independent unit from Madison County led by Capt. Frank Gurley. The Adjutant and Inspector General eventually authorized the transfer of Bacot's Battalion from Forrest’s Regiment on July 19, 1864.

The veteran in question said he served in Co. "H" of Russell's 4th Alabama Cavalry. This was the "Russell Rangers", led by Capt. Henry Milner, which organized at Guntersville Al on Sept. 15, 1861, and served in Forrest's Regiment as 1st Co. "H". It became part of Bacot's Battalion and was one of the four companies from that command to join Russell's 4th Alabama. I'm not at all sure what the January 1861 date represents; perhaps the veteran in question joined in January 1862.

Julian's Battalion is a different command associated with Roddey's 4th Cavalry, not Russell's. This command was an unorganized battalion serving in the Tennessee Valley during the first half of 1863. Captain William Reese Julian organized a cavalry company near Tuscumbia in the late summer of 1862 which joined Roddey's 4th Alabama Cavalry Regiment. Detached by the end of 1862, his men evidently operated for a few weeks with Patterson's 5th Alabama Cavalry. During the spring of 1863 Julian gathered several companies under his command, possibly with intent to raise a regiment.

Company "A" of Franklin County
Company "B" of Morgan County
Company "C" of Lauderdale County
Company "D" of Hardin County, Tennessee

About July 1, 1863, Julian's companies reported to Jeffrey E. Forrest's Confederate Cavalry Regiment. Captain Julian was appointed Ordinance Officer August 20, 1863, and assigned to the staff of General Roddey.

Colonel Jeffrey E. Forrest’s Cavalry Regiment formed on June 15, 1863, probably at Tuscumbia, Alabama, composed of companies from the unorganized battalions of Major George L. Baxter and Captain William R. Julian. Evidently there were no formal letter designations for companies until after September 30, 1863. Actual letter designations of Alabama units are uncertain, and may have changed more than once. These are my best guesses:

Company “A” of State of Tennessee
Company “B” of Morgan County
Company “C” of Franklin County
Company “D” of Limestone County
Company “E” of State of Tennessee
Company “F” of State of Tennessee
Company “G” of Franklin County
Company “H” of Lauderdale County
Company “I” of Lawrence County
Company “K” of Franklin and Lauderdale Counties

Colonel Forrest, the brother of General Nathan Bedford Forrest, was killed at Prairie Mound, Mississippi, February 22, 1864. His regiment was broken up by order of General Forrest on May 11, 1864. Four Alabama companies were assigned to the cavalry battalion of Major William H. Warren, while Tennesseans transferred to Newsom’s 18th Tennessee Cavalry Regiment. Although it had never formally recognized Forrest’s Regiment, the Adjutant and Inspector General confirmed these changes on July 11, 1864.

Warren's Battalion was eventually merged with six companies from a battalion led Major James T. Williams. Major Williams was killed at Courtland AL on May 27, 1864. The two battalions formed the 11th Alabama Cavalry Regiment (at least as far as the War Department was concerned) on February 13, 1865, effective January 14, 1865.