It is not permissible to keep embryos or fertilized eggs
There are different kinds of fertilization, some of which are halaal and some are haraam. The halaal types include:
(i)Where the sperm is taken from the husband and the egg from his wife, and fertilization is done externally, then the embryo is implanted in the wife’s uterus.
(ii)Where the husband’s sperm is taken and injected into the wife’s vagina or uterus to fertilize the egg internally.
The Islamic Fiqh Council has stated that this is permissible. See the text of their statement in the answer to question no. 23104.
It is not permissible to keep eggs or embryos, and the fertilization of eggs must be limited to the required number so as to avoid having an excess of fertilized eggs. If there is an excess of fertilized eggs, they should be left without any care to die naturally.
That is because keeping embryos or eggs may lead to them being mixed with others as time goes by, either by mistake or deliberately, as has happened in many cases. Some of them may be taken and placed in the uterus of another woman, which leads to confusion of lineages, which is a serious evil which outweighs the interests which the couple may think are served by keeping embryos to save money and use for fertilization later on.
The Islamic Fiqh Council belonging to the Organization of the Islamic Conference has issued a statement on this matter. The text follows:
1-In the light of what has happened of the possibility of keeping unfertilized eggs to be used later on, when fertilizing eggs it must be limited to the required number for implantation each time, to avoid an excess of fertilized eggs.
2-If there are any extra fertilized eggs – for any reason – they should be left without medical care until they die naturally.
3-It is haraam to use fertilized eggs in another woman, and sufficient precautions must be taken to prevent using fertilized eggs for an illegitimate pregnancy. End quote from Majallat Majma’ al-Fiqh al-Islami, issue no. 7, vol. 3, p. 563.
And Allaah knows best.