The ruling on a verbal will
I have a sister who passed away leaving four daughters. She has full brothers and sisters. She made a verbal will leaving the inheritance to her daughters. What is the ruling of Islamic law concerning this will and how is the estate to be divided?
The four daughters of the deceased receive an obligatory share of two thirds of the estate which is to be divided equally among them. This is because of their number and because of the non-existence of a male sibling. The siblings of the deceased receive the remaining one third, with each male receiving the equivalent portion of two females because they are universal heirs, due to the absence of any other person deserving an obligatory share and to the absence of a closer universal heir.
This only holds if the matter is indeed as mentioned in the question and if the deceased does not have heirs other than those mentioned in the question or other descendants who deserve an obligatory bequest.
The verbal will
If all of the deceased's siblings unanimously acknowledge the verbal will made by the deceased in favor of her daughters, then it obligatory upon them to implement it from all of their shares within one third of the estate. Any portion in excess of one third of the estate becomes binding by those who give permission for the excess but not by those who refuse to authorize it. However if all of the deceased's siblings refuse to acknowledge the verbal will, then it is of no consequence and is considered as non-existent. If only some of the siblings acknowledge the will, then only those who acknowledged it may execute it from their shareand this must be only within one third of the estate except if the consenting party wishes to give away a greater portion of his share.
Allah the Almighty knows best.