How is the inheritance distributed among a mother, a grandfather, a full sister, a paternal half-brother, a maternal half-brother, and a maternal half-sister?

The brother and sister from the mother's side do not inherit in the presence of the grandfather, by agreement of the jurists.

If the heirs are limited to the mother, the grandfather, and a brother and sister from the father's side:

1. According to the majority (inheritance of siblings with the grandfather): The mother gets one-sixth. The remainder is divided between the grandfather and the siblings (the grandfather's co-sharing is more advantageous here). The sister from the father's side takes one-half, and the brother from the father's side is excluded if nothing remains for him. The estate is divided into six shares: one share for the mother, two shares for the grandfather, three shares for the full sister, and nothing for the brother from the father's side. This is the method of Zayd ibn Thabit.

2. According to Abu Bakr Al-Siddiq and some jurists (the grandfather totally excludes the siblings): The mother gets one-sixth. The remainder goes to the grandfather. Nothing for the full sister or the brother from the father's side. This opinion is preferred by Sheikh Al-Islam Ibn Taymiyyah and Ibn Al-Qayyim, and Ibn Uthaymeen considers it the correct opinion because its details were not mentioned in the Quran and Sunnah.

The prevailing fatwa (ruling) is the inheritance of siblings with the grandfather.

Important note: Inheritance matters are complex and delicate, and a mere fatwa is not sufficient. They must be referred to Sharia courts for a thorough investigation of all wills, debts, rights, and heirs.