Is it permissible for a brother to take from his sister's interest-based money (which she will inherit and give out for the sake of Allah upon reaching maturity) in order to buy an apartment, on the condition that he considers it a debt upon himself to Allah that he will repay later, just as he did with his own interest-based money which he gave out for charitable causes?

Usurious bank profits are unlawful wealth that must be spent on public Muslim welfare or given to the poor and needy. A poor son who cannot find housing may take from these profits according to his need, and he is not required to return what he took if he becomes affluent. However, if the son is not poor, he is not permitted to take from this money, and it must be spent on charitable causes.