Complex sentence: By early May 1862, several of the companies of the the regiment were still in Arkansas with Colonel Rector, eventually becoming part of the 35th Arkansas Infantry Regiment, and the remaining companies were at Corinth, Mississippi, with the Army of the West.
Split into simpler sentences: By early May 1862, several of the companies of the the regiment were still in Arkansas with Colonel Rector, and would eventually form the core of a new regiment, designated the 35th Arkansas Infantry Regiment. The remaining companies were at Corinth, Mississippi, with the Army of the West.