Embryo transfer from genetic mother to surrogate has not been done in humans. It's easy in horses and cows, we do it all the time. In horses, it's become routine to breed very high performing mares, harvest the embryo, send the mare back out to compete and put the embryo in a cheap reproductively healthy mare to gestate...because a mare's best performing years and her best reproductive years are the same.

In humans we can do inward embryo transfer for IVF. However, the failure rate is fairly high. The reason why so many IVF births are multiples is because the cheapest/quickest option is to put several embryos in there. It's getting better, but embryo transfer still only has a 23 percent success rate for fresh embryos and an 18 percent chance for frozen.

Transferring an embryo from the biological mother to a surrogate has not been done in humans. This is in part because it would be impossible to do such research without destroying embryos which, obviously, raises ethical concerns. The pro lifers don't want the research to be done. So basically we have yet to harvest an embryo from one woman to put it in another. And to get anywhere, we have to be willing to do that research. Ironically, research that could significantly reduce the number of abortions by allowing for more prenatal adoption (prenatal adoption already exists, but under the more narrow circumstance of women who don't produce their own eggs adopting surplus embryos from somebody else's fertility treatment that would otherwise be discarded) is being blocked by the same people who want fewer abortions...