Can she make use of frozen embryos?
Praise be to Allah.
Artificial insemination, or what is known as test-tube babies, takes many forms, some of which are permissible and some are haraam. The permissible forms include cases in which the sperm is taken from the man and the egg is taken from his wife, and fertilisation takes place externally, then the embryo is implanted in the wife’s uterus.
In this case it is essential to take precautions and look for trustworthy doctors, for fear of tampering, because some doctors may use sperm that does not come from the husband when they already know that the husband’s sperm is not suitable for fertilisation; and there are other problems and evil consequences that may occur. See the answer to question no. 98604
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.
Based on that, what you have to do is dispose of the frozen embryos; it is permissible for you to undergo further artificial insemination even if that is costly or difficult, because that harm cannot be compared to the possibility of embryos being mixed up, especially since this length of time has passed.
And Allah knows best.