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Other entries show they were based near Potijze, near Ypres. On this map Potijze is marked with the arrow. So Matthew was presumably out with this fighting patrol when he was captured. They started about 500 yards south of Potijze, and attacked a post about 800-900 yards away, probably at Hussar Farm
If you click on the map it should open a larger image in a new window.
Cottbus is in Germany, close to the Polish border, so Matthew must have been transported some 1000km. I then started trying to find out about Cottbus, the POW camp in Prussia, and found an entry on the Red Cross site: http://grandeguerre.icrc.org/
Firstly on the 'Life in Internment Camps' tab I could see where Cottbus was, and that there were five camps in that area. Clicking on the map it took me to the visit report by ICRC on 18th December 1918, after the armistice. In particular it showed how many prisoners there were of each nationality, and almost all 1500 British POWs were in Cottbus 1. If anyone fancies translating it from French then I can provide the document as a pdf.
Also on the ICRC website are cards for each POW.
Matthew's card confirms his identity and points to an extra file PA 33350.
This shows the list sent by the POW Camp to the Red Cross with Matthew's details. I'm not a German expert, but it identifies him as a Corporal in Royal West Surreys, and I think it means C Company. I believe it says he was taken prisoner on 30 May 1918, (which matches my earlier investigation) at Ypres, and wasn't injured. Hirson is a place near Arras, so it is possibly where he was taken after being captured. It has his date of birth and next of kin.