Adrian,
Glad to help. I assume you have seen Cooper's file on-line:
https://recordsearch.naa.gov.au/Sear...?B=1056392&S=1
UPDATE:
Just to clarify, 576 Squadron was formed around Flight "C" of 103 Squadron in November 1943.
http://www.historyofwar.org/air/units/RAF/576_wwII.html
Thus Lancaster ED713 was apparently in 103 squadron (flight C?) through the summer and fall of 1943.
This link (search for ED713) shows the plane as being both in 103 and 576 squadrons.
http://www.lancaster-archive.com/lanc-noseart-m-o.htm
You mention that Cooper was a substitute for the regular navigator of the crew that was lost in July. Maybe the photo shows Cooper with a different 103 squadron crew, maybe his "regular" crew.