His father was missionary George Moule (1828–1912), the first Anglican bishop of mid-China.
Arthur Christopher was uncle to the famous Cambridge theologian and New Testament scholar C. F. D. Moule.
Moule was educated at The King's School in Canterbury and Trinity College, Cambridge.
In 1918 he received the living of Trumpington just outside of Cambridge, where he could continue his scholarly work on Chinese subjects.
[1] Moule died on 5 June 1957 in St Leonards-on-Sea, Hastings, England.