Is this money rightfully hers, and does she take it after her father's death, or is it distributed according to the legal inheritance?

A father must be just among his children in giving gifts, so he should give the male twice the share of the female, based on the saying of the Prophet, peace and blessings be upon him: "Be mindful of Allah and be just among your children," and according to the hadith (definition) of Nu'man ibn Bashir. As for maintenance, he gives each child what they need. So, if what the father gives his son is a gift exceeding maintenance, then he has done well by giving the daughter half of what he gave the son. But if it is maintenance, he should not give the daughter anything unless he gives the son the same. It is wrong for a father to bequeath to his young children an amount equivalent to his expenditure on their adult, married siblings, as this is a bequest to an heir, which is forbidden. If the amounts the father pays his son are gifts, then it is wrong for the father to place the daughter's share in the bank in his name for her to take after his death, because the money must be put into her possession, and because it is a bequest to an heir, and because taking loans and investing money in usurious banks is forbidden. So, if the father wishes to be just in giving gifts, he must put the money into his daughter's possession. If the daughter takes her share of this money after the father's death and it was her right, then there is no harm in that.