He was promoted to Lieutenant (temporary) on 13 September 1915, and is recorded as being with the 13th Service Battalion of the Rifle Brigade in the May 1916 edition of the Army List (column 1558b, if anyone's mad enough to look), and remained with that battalion until his move to the Coldstream Guards, as per above.
So in answer to
@mnairb's original thought, he
was promoted to Temporary Lt, but subsequently transferred to the CG as a 2nd Lt; he was the most senior 2nd Lt in 2nd Bn, and second-most senior in the regiment.