25c Pz M13/40 735(i) & Pz M14/41 736(i):
See Italian Vehicle Note 8 & Note 9. Both of these vehicle were used, to a limited extent, by German forces in Italy. Stocks of them had been seized following the Italian armistice and were then pressed into service. It was used in anti-partizan activity and one was sent to help quell the Warsaw uprising...with predictably poor results.
The Cruiser Mk IV A13 Mk II as the Kreuzer Panzerkampfwagen Mk.IV 744(e) were used as command tanks for Flammpanzer II (Flamingo) in Panzer-Abteilung (Fl) 100 in the USSR in 1941. It's the only case I know of where British tanks were properly incorporated in a first line German unit. Those were all from tanks captured in France '40. I suspect the earlier '40 captured Cruisers I-III didn't have either the speed or armour to be used for other than training or security roles. One Cruiser III A13 Mk 1 as the Kreuzer Panzerkampfwagen Mk III 743(e) was photographed near Siska, Yugoslavia in '43 or '44 (in the below site).
British tanks captured in the desert were mainly used "as is" by the Germans with only tiny handfuls sent back to Germany for analysis and research.