How is the inheritance distributed for a deceased man who left behind a wife, two daughters, and a paternal half-brother?

To our knowledge, it has no basis in the pure Sunnah, and Sunan are not established except with proof. Imam Al-Nawawi, may Allah have mercy on him, mentioned in his book Al-Adhkar the invocations for Safar, the beginning of Rajab, the middle of Sha'ban, the first ten days of Dhul-Hijjah, the Day of Arafah, the Day of Ashura, the White Days, and other days and circumstances for which specific invocations were reported. However, he did not mention anything regarding the night of the twenty-seventh of Rajab. Had it been legislated, he would have mentioned it, as he was among the most knowledgeable people concerning the Sunan and traditions. Some great imams, such as Sheikh al-Islam Ibn Taymiyyah and Imam Al-Shatibi, have denounced it. Consequently, reviving it and claiming its exclusivity for a specific act of worship is an innovation (bid'ah) that is not permissible, and it falls under the saying of the Prophet, peace and blessings be upon him: "Whoever introduces into this matter of ours that which is not from it, it will be rejected." (Agreed upon). And his saying, peace and blessings be upon him: "Beware of newly invented matters, for every newly invented matter is an innovation, and every innovation is a misguidance." (Narrated by Ahmad, Abu Dawud, Al-Tirmidhi, and Ibn Majah). The Eid of the Hijri New Year also has no basis, and what indicates this is that it did not exist during the time of the Prophet, peace and blessings be upon him, nor during the time of the noble Companions. Therefore, the Muslims' celebration of it is not part of the Sharia in any way. Sheikh al-Islam Ibn Taymiyyah, may Allah have mercy on him, was asked in Al-Fatawa Al-Kubra: Is gathering to celebrate the Mawlid and preparing food for it an innovation or not? He replied: "Praise be to Allah, gathering for that purpose is an innovation." Ibn Al-Hajj also transmitted in Al-Madkhal the dislike of some of the Salaf for it. Al-Shatibi said in Al-I'tisam: "Among the innovations that have been introduced are the celebrations of Mawlid Eids," and he mentioned the hadith: "Every innovation is misguidance." Al-Suyuti also alluded to this by saying: "Indeed, celebrating the Mawlid is an undesirable innovation."

And Allah knows best.