Hakdama 3 - Regarding Reincarnation, Yibbum, and Ibur. I saw fit to widen out this explanation of reincarnation, yibbum, and Ibur. Here, regarding Ibur, this [happens] during the life of a person (as explained in Hakdama 2). I wanted to say, that sometimes a person will merit through some mitzvah, and this makes a rectification.
And through this rectification, he receives another Nefesh from an ancient Tzaddik (which already departed from the world). This Tzaddik [has a similarity to him in that he also] did the same mitzvah, and when the person does the mitzvah, the Nefesh of the Tzaddik enters into him (like a pregnancy or an additional soul added onto him). Not only this [that this happens from a Nefesh of a Tzaddik that already departed from this world], but it is also possible that this happens when the Tzaddik himself is alive and found with him within this person's lifetime.
If this happens (that an Ibur of the Tzaddik happens when he is alive), the Ibur [of a spark of the Tzaddik's Nefesh] enters into him for the reasons we explained. So when this person does this mitzvah or mitzvot which are relevant to the Tzaddik that is with him in his lifetime, a spark of the Tzaddik's Nefesh enters into him, even though they are both alive at the same time. And this is the secret of the passuk, "Dovid's Nefesh connected to Yonoton."
Even though the two of them were alive together, Dovid's Nefesh implanted (Ibur) into Yonoton. However, with regard to reincarnation ("Gilgul"), we need to widen out this concept a bit. Thus, we will begin the concept from Adam haRishon (another editor will fill in missing parts):