Is the wife entitled to claim a debt that the husband wrote upon himself for her after their divorce, knowing that he wrote it to appease her during a dispute between them?

If the money stipulated for a wife's right was waived by her, she has the right to claim it judicially. However, if it was merely a compensation, it is a promise of a gift that is not binding except upon possession. She can ask him to fulfill the promise, but she cannot claim it judicially.