Hi Gott61,
I know nothing about Army regimental badges, but there are several members here that do. Br aware that 60% of WW1 other ranks records were destroyed in a fire during WW2. Confirmation of regiment would be a start. He was certainly born in 1889, but I have not found a serviceman of that name, birth year & Coventry listed in surviving records. However, he will most likely exist in the WW1 Medal Rolls, but we need a regiment & service number to separate him from all the other "Arthur Moore"s.
On the 1911 Census, he was the only child of John & Emma still living at home at Charterhouse Mill, Coventry, his occupation being a carman & his father being a miller. If you are living in or near Coventry, the 1918 Absent Voters List will give his regiment & service number. Either Warwickshire Archives or the main library in Coventry should have a copy. Other members will no doubt be able to add further information in due course.
Maurice