Hi Elmar,
in the "Luftwaffe Officer Career Summaries" by Henry L. deZeng IV and Douglas G. Stankey, both active in this forum, you find the following entry :
"KESSLER, Hugo. 01.06.42 promo to Hptm. 10.11.43 appt Ia op 1/7. Jagddivision. 01.45 Hptm., Leiter Gruppe 1/General der Jagdflieger. 01.05.45 Hptm. and Adj. in JV 44."
see also
http://www.ww2.dk/Lw%20Offz%20-%20G-...Apr%202016.pdf
In the JV44 pilot list of 27th April 1945 Hptm. Kessler is not mentioned.
As adjutant/ "right hand" of Galland he was in charge of many organizational tasks of JV44.
Do you know whether your father had a Pilot licence?
Best regards, Karl