1. in a way that is morally right, just, or deserved
2. according to what is legally or officially correct

Examples

• She rightfully deserved the promotion after years of hard work.
• The property rightfully belongs to his family.
• He was rightfully angry about the unfair treatment.
• The championship trophy rightfully went to the winning team.
• They rightfully demanded an explanation for the mistake.
• The inheritance rightfully passed to the eldest son.
• She rightfully claimed credit for the successful project.