It is not permissible to insert the water of a foreign man into the vagina of a woman, and as for the fertilization of the extraction of the egg from it, it is not permissible because it requires exposure to the foreigner, whether man or woman, but if the woman commits this forbidden, then the fertilization of the egg externally with the sperm of a man other than her husband, then implanting the fertilized egg in Her womb is a matter of disagreement among the jurists, and Sayyid al-Sistani, may God protect him, says that it is permissible because there is no evidence of inviolability.
However, the child born from this process does not join the woman's husband, nor is he attributed to him, nor are they inherited.