Complex sentence: He enlisted into 34 Company Army Service Corps in the rank of conductor on 10 August 1900 and remained with the unit through until 19 February 1901 when he transferred at his own request to the mounted unit Rimington's Scouts and Guides.
Split into simpler sentences: He enlisted into 34 Company Army Service Corps on 10 August 1900. Holding the rank of conductor, he remained with the company until 19 February 1901 when he was transferred at his own request to a mounted unit, Rimington's Scouts and Guides.