'To fag'

'To fag' - we think we know what the slang term means; to serve an older boy, in the dodgy setting of a British Public School. But there was another use; an article in the Arbroath Herald, 4 Oct 1918, reads as follows:

After the band had bestowed its benediction in the strains of "Return to Serbia," the writer was fortunate enough to "fag" an interpreter, through whom he sought out the native Scoutmaster.

This seems to show 'fag' being used as a verb, meaning 'get hold of'. In The Grey Brigade ( a trench - actually camp - magazine of a group of London-based territorial regiments) on 26 June 1915 we find:

 

What is to be done with the inveterate cigarette obtainer - the man who always has a box of 50 in his kit-bag but none in his case? He is to be found in all companies. "Got a fag, old man?" is the favourite opening. The only way of escape, it seems to me, is to form an S.F.C.O.U.F. - Society For Choking Off Undesirable Faggers.

So, does 'to fag' come from the word 'fag' for cigarette, and mean originally 'try to get a fag', and from this 'try to get something for nothing', and then to 'manage to get something'?