Should it be of interest, his younger brother, Herbert Harold Robbins, joined the Tank Corps in 1919. His mother wrote and asked that he be discharged. The army refused as he was over 17 when he joined up (if a man was serving in a technical corps that was the age rule). He was however discharged in 1920 with defective eyesight, later joining the West Yorks Territorials, attending annual camps in 1923 to 1927 and later still transferring to the Royal Field Artillery Territorials. His records are on Ancestry.
The letter from his mother has another minor clue to his brother. It is dated 13 Jun 1919 and states that the brother is in Russia. She also states that he (the brother) has been in the army for 2 years 6 months. That may solve the mystery of another document not mentioned so far found on FindMyPast which is the attestation record of Arthur Nelson Robbins at Bradford on 13 Feb 1917 (about right) although, to make that even more frustrating, that record says he was transferred to the Royal Flying Corps. No subsequent RFC or RAF record has been found (yet!). There is where he lied about his age, stating he was 18 years and 33 days old! However, his birth was registered in Q2 1900 (his mother confirms he was 19 in 1919) so he was actually 16 and a bit when he joined up. She also says that she is "on her own" - one wonders whether the father, also Arthur Nelson Robbins, was in the army still at that date? He was about 45 at war's end, not impossible.
However (again), despite the tantalising clues, there can be no real progress without a service record.
maxD