I've also found a 1911 cencus with Arthur, his mother Emma and a Nellie Calcott, if Nellie became is wife I don't know.Believe he survived the war, but he seems to have been sent to Coventry by the family, for reasons unknown.
I've found one 2584 Arthur Moore that may be him but can't find anything concrete to link him yet.
Another lead maybe sub district in Coventry could be Holy Trinity or St JohnI've also found a 1911 cencus with Arthur, his mother Emma and a Nellie Calcott, if Nellie became is wife I don't know.
It looks very much like it the Worcesters is a very distinct starCould be a Warwickshire Regiment cap badge as the Worcester Reg has a Star emblem. Took a snip from your photo and distorted a copy of an original cap badge - any views?
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Beake Avenue is a very long road in the Radford district if this is of help.I think I've found him in 1939 living with a lady called Elizabeth 139 Beak Avenue Coventry
She is older with two children of a different name,
This maybe why the family had nothing to do with him,
Defiantly a Warwicks badge, no doubtIt looks very much like it the Worcesters is a very distinct star