Is it permissible for this woman to falsely swear by Allah to save her family, in order to obtain aid from the Ministry of Social Affairs, knowing that one of the conditions for obtaining it is that she must swear that she has not remarried after her divorce from the first man?

Lying is a grave sin and a reprehensible trait. Its ugliness is compounded when it is combined with swearing by Allah. The Prophet, peace and blessings be upon him, permitted lying in three situations: reconciling between people, war, and a man speaking to his wife or a woman to her husband. Scholars have appended to these pressing necessities, such as saving a Muslim's life or property, provided that the commendable objective cannot be achieved except through lying. It is more cautious to use ambiguity in speech.