Embryo Adoptions

Hello Masters and Teachers, I was reading about the never-ending debate of anti-abortionist vs. abortionist. One of the points that they brought up was, what to do with the extra embryos that are used to help impregnate couples with fertility problems? One argument (the abortionists) was to destroy the embryos! The second opinion (anti-abortionists) was the adoption of these embryos to other couples with fertility problems! My question is what does that do to the embryos that are Jewish? If these clinics are sending out these Jewish embryos, is there an agency that checks to see that they are going to Jewish couples? Does the Jewish connection start at the level of the egg? Thank you for your time. Chag Sameach

There are differing halachic opinions regarding whether or not the identity of the genetic mother determines if a child is Jewish (Nishmat Avraham IV Even HaEzer 5 2; Nishmat Avraham V Even HaEzer 5 5).