'His effects were distributed to his Widow Annie Murray and Daughter Catherine - very interesting that his son Thomas William Murray (born 1912) was not listed??? THOUGHTS would this be because he is under 18 years (?) or does this possibly give the thought that he MAY NOT be recognised as his son (Thomas is on his birth certificate as father). '
Highly unlikely that it would be because he is not his son. What was Catherine left - a small memento or something substantial? As you said Thomas was only 6 or 7.
'I cannot find any information on Annie Murray from 1912 to her death in 1943 in Coulsden appart from mention as widow on Thomas Military records of personal effects distribution. '
What sort of records are you looking for? If she lived where the ER's are not on-line, and never remarried, or never did something note-worthy enough to be published in a newspaper, she would maintain a low profile.
Have you tried a trial membership of Ancestry (or you might need fold3) or F M P?
'James Murray (1855-?) married Caroline Elizabeth Dial (Dialls)'
Where was he born from censuses, and who was his Father from marriage certificate?
Added:Is Caroline Elizabeth showing as Elizabeth on 1881 and 1891?