Is it permissible for children to inherit from the estate of their father's wife if that estate originally belonged to their father, who bequeathed it to his wife before his death? And how is it to be divided then?

A will in favor of an heir is not permissible, based on the Prophet's (peace be upon him) saying: "There is no will for an heir." The father's wife is among the heirs, so her share of your father's estate is only one-eighth. Anything in excess of that is the right of the (children) heirs, unless the adult heirs approve this will, in which case its execution becomes permissible.

As for what your father's wife left after her death, it is divided as follows:

1. Her private wealth is divided among her legal heirs. 2. The gift your father bestowed upon her during his lifetime and which she took full possession of is considered part of her private wealth and is divided among her heirs. 3. Her legal share of your father's estate (one-eighth) is distributed among her heirs. 4. Any amount exceeding her legal share of your father's wealth, whether he bequeathed it to her or not, is your right as (heirs) and is divided among you according to Islamic law. It is permissible for you, if you are adults, to waive a portion of it for her.