Hello bookman,
according to that website
http://ww2.dk/oob/bestand/jagd/biijg77.html
II./JG77 was fully equipped with the Macchi M.C.205 from October until December 1943.
Three of Reinert's claims are in this time frame: 22,10.43 - 6,11.43 - 7,12.43
Michael