What is the ruling of Islamic law regarding the distribution of our deceased brother's blood money among the legal heirs, taking into account the death of our sister after the incident and her leaving behind children, and the presence of a maternal half-brother?

The blood money (diyah) for the slain is considered part of his estate and is distributed among his living heirs after his death, based on the hadith: "Indeed, the diyah is an inheritance among the heirs of the slain according to their kinship, and whatever remains is for the 'asabah (agnatic kin)." Debts and bequests (up to one-third) are paid from it, and the remainder goes to the heirs. It is not permissible for the guardians of the slain to pardon the diyah if he was in debt, because their right does not precede the debt. The share of the sister who passed away after him is given to her heirs. The deceased's estate (including the diyah and other assets) is divided as follows: the mother receives one-sixth, the brother through the mother receives one-sixth, and the remainder is for the brothers and sisters by 'asabah, with the male receiving the share of two females.