A hot candidate for Luftwaffe´s last kill is Oblt. Fritz Stehle, Staffelkapitän of 2./JG 7 who claimed a Jak-9 late in the late afternoon on 8 May 1945 over northwestern Bohemia while retreating with his Me 262 from Žatec to Fassberg. It seems that he actually shot down an Airacobra, whose pilot, mladshiy leytenant Sergey G. Stepanov of 129 GIAP (22 GIAD) crashed to his death near the village of Kliny. Parts of Stepanov´s Cobra were later recovered - you can see some fragments from his aircraft as well his grave on:
http://www.plarchiv.eu/nalezy/nalez14.htm
If the question was meant to be about the last WW2 claim in Europe, let me add that some USAAF (and probably also VVS) claims were made even later...
Hope this helps a little,
Ota