Is it permissible for a mother to transfer the amount of social security that was deposited for her—while she is not in need of it and did not add her husband's data—to her needy brother, or must she return it to social security?

Your mother must return the money to Social Security and abide by their directives. She is not permitted to dispose of it, for Allah, the Almighty, says: "O you who have believed, fulfill [all] contracts," and the Prophet, peace be upon him, said: "Muslims are bound by their conditions." Furthermore, it is not permissible to consume wealth unjustly, for Allah, the Almighty, says: "O you who have believed, do not consume your properties among yourselves through falsehood." As for your uncle, he can apply to Social Security himself if he is eligible.