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 heir other than his wife and his sister, i.e. there are no other heirs who are entitled to legitimate shares or by Ta’seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); then the inheritance should be divided as follows:
His wife gets one-fourth as her legal share due to the non-existence of children (direct heirs); Allaah says (what means): {And for them [i.e. the wives] is one fourth if you leave no child.} [Quran 4:12]
His sister gets half as her legal share as she is the only heir [after the wife] and there are no other heirs who are entitled by Ta’seeb to the inheritance. Allaah says (what means): {If a man dies, leaving no child but [only] a sister, she will have half of what he left.} [Quran 4:176]
Also, the sister gets the remainder of the inheritance after deducting the allotted shares because there are no other heirs who are entitled to participate with her in the division of inheritance by Ta’seeb. Allaah says (what means): {But those of [blood] relationship are more entitled [to inheritance] in the decree of Allaah.} [Quran 8:75]; so the remainder is not given back to the wife because she is not among the blood relations of the deceased.
Therefore, the inheritance should be divided into four shares, the wife gets one-fourth, which is on share, and his sister gets three shares.
Allaah knows best.