Thanks to the inheritance his father left, he can live comfortably.
Literal
Father's left property [thanks to-のおかげで] he [topic-は] comfortably can-live.
~のおかげで means 'thanks to / because of (a positive cause).' 残した is a relative clause modifying 財産 ('property/inheritance'). 楽に暮らせる uses the potential form: 'can live comfortably.'