All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the deceased did not leave any other heirs except those mentioned in the question, and the hermaphrodite is a half sibling from the father meaning that he is a sibling from the father only and not a full sibling or a sibling from the mother only, then all the inheritance is for the full-brother of the deceased by Ta’seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so he gets all the inheritance or what is left after the allotted shares have been distributed); and the hermaphrodite does not get anything because the paternal half sibling whether it is a brother or sister, does not inherit if there is a full-brother.
If the hermaphrodite is from the mother only, meaning that he is neither a full sibling or a paternal half sibling, then he gets one-sixth as his legal share, whether he is a male or a female as Allaah Says about a half sibling from the mother (what means): {… but has a brother or a sister, then for each one of them is a sixth…}[Quran 4:12] The remainder is for the full-brother by Ta’seeb as the Prophet said: “Give the prescribed share of inheritance to those who are liable for it and the remainder [of it] is for the nearest male blood relative." [Al-Bukhari and Muslim]
In case the hermaphrodite is a sibling from the same father and mother – a full-brother or a full-sister – then one of the two following cases applies to him:
1- If he is a discernible hermaphrodite, meaning that it is clear whether he is a male or a female, then, in this case, he should be treated according to what he is; if he is a male, then the inheritance should be divided into two parts between him and his full-brother, half for him and half for the other brother. In case he is a female – a full-sister – then the inheritance should be divided into three shares, the full-brother gets two shares and he (the hermaphrodite) gets one share as Allaah Says (what means): {If there are both brothers and sisters, the male will have the share of two females.}[Quran 4:176]
2- If his matter is not yet known whether he is a male or a female, then the full-brother and the hermaphrodite should be given the least share of each of them because this is the certainty (at the moment) and the remainder should be kept aside until the case of the hermaphrodite becomes clear. The least share of each of them means that the hermaphrodite is considered as a female. Therefore, the inheritance is divided into six shares, the full-brother gets three shares (because it is probable that the hermaphrodite is a male), and the hermaphrodite gets two shares (assuming that he is a female), and one share would be kept aside. Afterwards, if it becomes clear that the hermaphrodite is a male, then the remaining share is given back to him, but if it becomes clear that he is a female, then the remaining share is given back to the full-brother.
However, if the hermaphrodite still remains an intractable and problematic (or what is called in Arabic a "Khunth Mushkil"), and his matter is not likely to become clear, then the full-brother and the hermaphrodite may agree among themselves in regard to the remaining share, and this is the opinion of the Shaafi’i School. As regards the view of the Hanbali and Maaliki Schools, the hermaphrodite should be given half of the share of a male and half of the share of a female, and according to their view, the share that is kept aside should be divided equally between them.
It appears that the view of the Shaafi’i School is the most correct one because giving the hermaphrodite half of the share of a male and half of the share of a female is a matter of Ijtihaad (personal judgment) which is not supported by a Sharee’ah text, whereas the Sharee’ah encouraged reconciliation in cases of stinginess; as in the statement of Allaah about a wife and her husband (which means): {…there it no sin upon them if they make terms of settlement between them — and settlement is best. And present in [human] souls is stinginess.}[Quran 4:128]
Besides, a Hadeeth attributed to the Prophet reads: “Reconciliation is permissible between the Muslims.” [Abu Daawood, At-Tirmithi and others] Therefore, it is better for them to reconcile about the remaining share rather than imposing on them a division that is not stated in any Sharee’ah text.
Allaah Knows best.