How is the estate of a man who died leaving a maternal half-brother and a full sister's daughter divided?

The nephew and niece (son and daughter of the sister) are considered kindred (dhawu al-arham) and are not heirs when there are sharers (ashab al-furud) or residuaries (asabat) present. The brother from the mother's side inherits the entire estate. One-sixth is a prescribed share (fard), based on the Almighty's saying: "And if a man or woman leaves no heir but has a brother or a sister, then for each one of them is a sixth." The remainder is taken by way of رد (radd - return), based on the Prophet's (peace be upon him) saying: "...and whoever leaves behind wealth, it is for his heirs." The matter should be referred to the Sharia courts or discussed with scholars to verify the heirs, wills, debts, and other rights before dividing the inheritance.