Is it permissible to benefit from a monthly financial aid designated for permanent residents in their country by claiming permanent residency in the father's house, knowing that I have traveled with my husband to his country, and that this aid would provide social security?

The criterion for the permissibility of benefiting from the assistance is the conditions set by the granting authority. If the assistance is designated for those who already reside in the city, then the questioner is not entitled to take it. However, if it is given to those who have obtained residency in the city, even if they do not physically reside there, then he is entitled to benefit from it.