WWII KIA ??

I am researching a WWII soldier Robert E. Kain who was with the 116th Inf. Regt. 29th Inf. Division.His homestate was Pennsylvania, Allegheny County.He was killed in action in June of 1944.He was first buried in La Cambe, France and reburied in a private cemetery in Pennsylvania.What I am trying to find out is the exact day he was killed.My research shows it was between June 6th and the 14th.I have searched many other sites and made many phone calls but have hit roadblocks.Any help on his exact date of death or where he is know buried is appreciated.

Thanks,Roger