Can a woman use another woman's ovum so that she becomes pregnant and then give birth to a child?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is strictly Haram to use an ovum of another woman (i.e. not your wife) to enable your wife to beget through artificial impregnation. Since an embryo comes into being due to integration of male's semen and female's ovum, this means that if your wife becomes pregnant because of using another woman's ovum, the child will not be yours.
The Fiqh Assembly prohibited such an action in its decision No. 16 (4/3) issued in 1407 A.H - 1986 A.C.
The decision reports that: 'The following five methods (of artificial impregnation) are prohibited in themselves or due to results such as: intermixing of lineage, loss of maternity and other reason, that Sharia rejects'.
First, carrying out the artificial impregnation between an ovum of some alien woman and semen of a man who is her husband, and then, implanting that fertilized ovum into womb of this man (husband)'s wife. …..
Fifth, performing the artificial impregnation between seeds (semen and ovum) of two spouses, and then, implanting the fertilized ovum into the womb of another wife.
Allah knows best.