Embryo transfer is done today as In Vitro Fertilization (IVF) or Zygote IntraFallopian Transfer (ZIFT) and in both processes, embryo is developed outside the womb and then placed inside.
Even in surrogation process, a woman takes fertilized eggs of another woman and grows the embryo in her womb until she delivers the child. Embryo transfer from a woman to another woman’s womb is yet to be experimented by modern science. Bhagavata Purana, written around 3100 BCE describes an incident, where two fully grown embryos are exchanged between wombs of two mothers and then delivered.
In Skandha 10, Adhyaya 2, that when Kansa killed all the earlier six foetuses of Devaki, the wife of Vasudeva,then at the seventh time of pregnancy, Shesha (the serpent of Lord Vishnu) came into Devaki’s womb.
It was quite possible that this foetus was also killed by the king Kansa.
So the transfer of foetus was arranged by Vishnu. He ordered his Yogamaya to take out the foetus of Devaki and place it in the womb of Rohini, another wife of Vasudeva who then resided in the house of Nanda in Gokul.
Devaki and Vasudeva were in a jail of Kansa, because an oracle predicted the death of Devaki’s evil brother Kamsa at the hand of “the eighth son of Devaki“. Kansa planned to kill all the progeny of Devaki immediately upon their birth, and imprisoned the newly-wed couple.
So, Vasudeva’s first wife Rohini was left alone under the care-taking of Nanda.
Yogamaya performed that great job of embryo transfer between Rohini and Devaki.
So, Balarama was born to Rohini and Yogamaya took birth as devaki’s 7th child. When Kansa tried to kill it, she escaped from his hands and warned him about his upcoming death in hands of Devaki’s 8th child.
Later Krishna was born as Devaki’s 8th child and was immediately transfered to Nanda’s house by Vasudeva during same rainy night.
That is how Rohini became the surrogate mother of Balarama (first in recorded history or literature) and the mother of Subhadra, while Devaki was mother of Krishna.
In modern era, 1979 has witnessed world’s first test tube baby, Louise Brown, born to Leslie Brown.
There has been many such test tube babies in later years but embryo transfers between wombs of two human mothers is yet to be done.
Embryo transfer in animals is also done similar to humans, but embryo exchange is yet to be tried.