All perfect praise be to Allah, The Lord of The Worlds. May His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Giving birth unnaturally by means of artificial insemination isn`t permissible save in case of necessity. Accordingly, the egg must be taken from the wife and the sperm must be taken from the husband, then the fertilized egg must be planted in the uterus of the wife herself. All of this must take place while the couple are actually living together by virtue of a valid marriage contract.
Article, (157/B) of the Jordanian Personal Status Act states: "A child`s affiliation to his/her father isn`t established save through:
1-The marriage bed
2-Declaration of paternity
3-Witness testimony
In conclusion, it is forbidden for a woman to conduct artificial insemination after death of husband and conceal his death to complete that procedure. This is because marital relationship ends by divorce or death of spouse. And Allah the Almighty knows best.