What is Church teaching on embryo adoption?
The closest the Church has come to addressing this specific issue was in the document Dignitas Personae:
It has also been proposed, solely in order to allow human beings to be born who are otherwise condemned to destruction, that there could be a form of “prenatal adoption.” This proposal, praiseworthy with regard to the intention of respecting and defending human life, presents however various problems not dissimilar to those mentioned above (19).
However, the USCCB did not see this as a definitive decision:
Proposals for “adoption” of abandoned or unwanted frozen embryos are also found to pose problems, because the Church opposes use of the gametes or bodies of others who are outside the marital covenant for reproduction. [Dignitas Personae] raises cautions or problems about these new issues but does not formally make a definitive judgment against them.
Theologian Fr. Tadeusz Pacholczyk notes in his article What Should We Do With Frozen Embryos:
There is ongoing debate among reputable Catholic theologians about this matter, and technically it remains an open question. A recent Vatican document called Dignitas Personae expressed serious moral reservations about the approach, without, however, explicitly condemning it as immoral.
For both sides of the debate, I recommend:
Dignitas Personae and the Question of “Embryo Adoption” A Debate on Dignitas Personae