I wonder whether it would be possible to transfer a fertilized egg to a surrogate mother.?

I have always felt that when girls unintentionally get pregnant, they are caught between a rock and a hard place because, firstly, they don't want the baby and, secondly, their parents will probably kill them if they found out. So, for them, the option is almost always to have an abortion which, needless to say, can cause a girl to become traumatized long into womanhood. Of course the simple solution is to tell girls to keep their legs closed, but mistakes happen, and besides pregnancies also require that boys' zippers get undone.

So, I was wondering whether it is possible for a girl who gets pregnant to have the zygote transferred to a mature surrogate mother so that she can carry the baby instead. I realize that the zygote is pretty small but if technology could be used to find it, is that an option that a girl in this situation would prefer? At least this would prevent the girl from terminating a viable life, and once the baby is born, it could be adopted.

I'm just wondering because if I was a girl, became pregnant and then terminated the pregnancy, I think it would bother me because I would always wonder what would have become of that baby. I would like to hear what girls think about this because I know that a significant number of girls terminate their pregnancies early.