What is not credible about this?
That does a great job of spelling out both sides.
I think what you are asking is "when is there a new soul present", which is not a scientific question. Scientifically, the banana I am eating for breakfast is still alive - the cellular processes are still occurring and changing. Scientifically, the kidney a woman donates, or the breast lump she has taken out, or an embryo she casts out with a medication abortion are all similarly alive. The intracellular reactions are still running.
The thing that differentiates these is the belief in a soul, which is a religious or philosophical matter. People can make up their minds about what they believe about these philosophical things based on their gut feelings, or what their parents or pastors say, or what came to them in a dream.
Stephen Jay Gould wrote a brilliant book "Rocks of Ages" which discusses the essential foolishness of the "fight" between science and religion. They only butt heads when they try to tell eachother how to do what they do - but looked at calmly, they each speak powerfully to their own field. He was a devout catholic and a world-renowned paleontologist. Check his book out - it's a quick read.