Is it permissible to agree to the marriage of one's sister to her disreputable and deceitful paternal cousin, who was previously rejected by other women, and from whom problems and lies emerged after the first engagement, and who then returned to propose to her after a long hiatus, knowing that the sister has no other marriage prospects?

You are obligated to refuse your sister's marriage to your cousin, especially given his lying and negligence in his responsibilities. Lying is丑恶 and contrary to faith; whoever lies once will lie repeatedly, and such a person is not suitable as a husband.

Allah’s Sharia (definition) legislated the guardian's approval for marriage because a man is more capable of choosing what is best for his ward. "Marriage is a form of enslavement, so let each of you look to where he places his precious one." And, "Marry her to one who fears Allah; for if he loves her, he will honor her, and if he dislikes her, he will not wrong her." And, "Whoever marries his precious one to a wicked person has severed her kinship."

Do not marry your daughter to an oppressor or a wicked person, for that is a crime against your religion and exposes you to Allah's wrath. One who persists in wickedness should not be married.

Reject him with a kind refusal while admonishing him, for it is better for a woman to delay marriage than to live with a corrupt husband.