six months (left) to live

Both are correct. "Six months to live" sounds slightly better to me.

Anything like that is an estimate, not an exact figure, and your sentences sound more definite than the situation actually is. You might want to say something like "His estimated life expectancy is about six months". My brother-in-law was diagnosed with liver cancer and was told he probably had about six months. He lived 19 months.

It is best to say "he'll be dead in six months so let's divide up his belongings now!"