I am trying to say that he came to terms with death but in a more formal way. How can I put it? Is conciliate the right word to use?
A couple of other phrases for the concept you're describing:
"he's resigned to his fate"
"he's reconciled to his imminent death"
"he's at peace with his own mortality"
People don't say either. Google N-grams reports no use of either phrase. Even a Google search of the phrases nets you less than 50 results for either.
"To come to terms with death" is a great phrase that carries a powerful connotation. But, other similar phrases are "move past" and "adapt."
- accepted ...
- came to accept ...