then a full sister or a paternal half-sister inherits, as a residuary heir, whatever remains after the prescribed share of one daughter or more. That is, when daughters are joined by full sisters or paternal half-sisters, give the daughters their allotted share, and the remainder goes to the sisters as residuary heirs.
For example, if a deceased person leaves behind two daughters and two full sisters, the two daughters receive two-thirds, and the remainder goes to the full sisters as residuary heirs. If he leaves behind one daughter and one full sister, the daughter receives one-half, and the remainder goes to the full sister as a residuary heir.
In summary, whenever daughters inherit alongside full sisters, the full sisters are residuary heirs alongside another. Hence, the scholars say: “Sisters alongside daughters are residuary heirs,” though they are residuary heirs alongside another.
Accordingly, I say: the scholars—may Allah have mercy on them—have divided residuary heirs into three categories: residuary heirs in their own right, residuary heirs through another, and residuary heirs alongside another. Residuary heirs through another comprise four categories: daughters, sons’ daughters, full sisters, and paternal half-sisters, when accompanied by a male counterpart equal to them in degree and category. This is based on Allah’s saying: “Allah instructs you concerning your children: for the male is a share equal to that of two females” [4:11]; and His saying: “And if they are brothers and sisters, male and female, then the male shall have the share of two females” [4:176].
Residuary heirs alongside another are only of two categories: full sisters and paternal half-sisters, alongside daughters or sons’ daughters. Why did the scholars distinguish between “through another” and “alongside another”? “Through another” is clear, because the preposition indicates causation: these women became residuary heirs because of others. As for “alongside another,” there is no causal agent, but there is companionship: full sisters are not made residuary heirs by daughters or by men; rather, they become residuary heirs through their association and accompaniment in the same inheritance case.
The residuary heir in his own right has a dedicated section, which will come, if Allah wills.