A search of an
applicable AWM database for "Burchell" does not indicate any who may have the initials "G.H.". One possibility (and the perhaps closest?) is for a "
Clive Harold Burchell" of the 32nd Australian Infantry Battalion who was reported missing in action in July 1916.
A quick look at his attestation paper suggests a possibility that, in his penmanship, his initial "C" could be mistaken for a "G".
https://recordsearch.naa.gov.au/Sear...aspx?B=3166869