What is the ruling on a marriage that is not legally documented, with the wife being aware that it entails no rights for her from the state, the purpose of which is for her to retain her pension from her first husband?

It is not permissible to deceive the state to receive a widow's pension after her marriage, because it constitutes consuming wealth unjustly. For a marriage to be valid, it requires the consent of both spouses, the presence of the guardian and two witnesses, the absence of any impediments to marriage for both spouses, and the contract is concluded with offer and acceptance. Documenting the marriage in court is obligatory to preserve rights, prevent disputes, and avert the harms resulting from a lack of documentation.