The Mother (Trinity) in Phantasy Star Zero is a generation of the folks of the fairly Earth-like Coral, again as a system to PSO2 Meseta manage and conserve the planet. At some point, she is tainted by Dark Falz, and it warps her to the point her directive of"preserve the world" makes her think that the ideal way to do so is wipe out all life on the planet so it can not ruin it and drain its resources, and prior to the beginning of the game, '' she razes the planet and wipes out most organic life, also wipes out the memories and melts down many CASTs.
Not too much a reincarnated personality, only a character by the same name that has some similar overlapping origins to preceding"Mother" characters in the show... I may have details wrong here, but the rough jist of these recaps is about right... I feel that the Mother (Brain) from Phantasy Star II is a generation of a race of"Earthmen" people, designed to restrain the starsystem's resources such as the reasonably Earth-like Palm, but is eventually tainted by Dark Falz/Force. Under her opinion, Palm ends up becoming destroyed by rapping with a satellite.
The core game design, a sprinking of buy Phantasy Star Online 2 Meseta names/concepts from the show beyond, along with peppy sci-fantasy with technical-magic, laser guns, and laser swords. The first PSI-IV are their continuity. PSO1 is its own continuity, with the strong implication PSZero a part of itbut it's possible it may be its own continuity too. PSU/PSP/PSP2 are their own joys. PSO2/PSNova are their own continuity. It's a string that shares conceptual elements, kind of.