He was an ardent atheist who underwent a deathbed conversion. The person who administered the last sacraments to him - Father Anselm Strittmatter - said that he was so terrified of dying that he did his best to distract himself from that prospect. Even spending time reciting Goethe's Faust to his brother.
He was a brilliant man and he was understandably terrified of the very mortal fate that awaits all of us.
However it has been reported, that he really did not handle the realization that he was going to die very well.
How exactly that handling manifested I have been unable to find.