[Rough Translation] And know, that after an Adam (a person) merits to take his Nefesh, Ruach, and Neshama, and then he damages (blemishes) them though a sin ('chet' meaning, something missing), [he blemished his Nefesh, his Ruach, and his Neshama], he must then return in a gilgul (in a reincarnation) to rectify what he blemished. When he comes back in a gilgul, he gets only his Nefesh [in the new body].
However, because he blemished his Nefesh, his Ruach is unable to enter his new body and to come with it. Even if he rectified the sin which blemished the Nefesh, it is not possible for a blemished Ruach to join him in this lifetime, because the Ruach also was damaged from his sin, so how can a blemished Ruach rest on a rectified Nefesh? So this Ruach comes in a gilgul into another person -- usually into the Nefesh of a Ger (which has a brand new unblemished Nefesh).
So too with the Neshama. Once the Nefesh is rectified completely, he is able to receive a Ruach, [but because his own Ruach is either blemished (damaged), or it is in the body of another person who is in the process of rectifying it], another Ruach (e.g., the Ruach of a Tzaddik which has a similar soul source as he) will come to him. Through the Tzaddik joining his Ruach to this person, the Tzaddik takes part in the good deeds that this person does (and the Tzaddik's own Ruach is elevated from this interaction).
Similarly, [in the next gilgul where he receives his Ruach (once it is rectified in the previous gilgul), because he also damaged his Neshama, it is either in a blemished state [so it is incompatible to join the Nefesh and the Ruach], or it could be in the body of another person getting rectified through their actions. While this is happening,] this person can receive a Neshama of a Tzaddik (and the Tzaddik also benefits from the elevation that occurs from this interaction).
This is the secret where it is said that "Tzaddikim are greater in their death, more than during their lifetime, etc." And here, when this person dies from the world, his Nefesh goes with the Ruach of the Tzaddik [e.g. to the high level of Gan Eden that the Tzaddik is at], and this way, he receives [a greater level of shefa ('G-dly radiance')] which is of the level of the shefa that the Tzaddik receives at his higher level.
When his own Ruach comes from the gilgul in which it was in the other person [e.g., the ger who was rectifying it, once he dies] the Nefesh of the Ger (who rectified his Ruach through his good deeds) [joins him at his level], and the first Nefesh (his Nefesh) says, "I will go and return to my first husband," and it joins with the Ruach (which was just rectified by the Ger). Similarly, the Neshama re-joins the Nefesh and the Ruach in the same way.