I liked this story, it is very thought provoking. However, I do not agree with the conclusions of the characters. It left sort of an icky aftertaste in my mind. I can understand the desire to pass on one's thoughts and memories, but I do not believe this system of reincarnation (assuming it works as well as in the story) would be beneficial, beyond the normal passing of information and culture to the next generation. It would make more sense to me without the denial of a soul. Sexual reproduction gives populations a greater ability to adapt to changing environments than asexual reproduction. In a similar sense as gametes, cultures are recombined, they change and adapt as they are transmitted to the next generation which allows them to survive in new forms when they otherwise may have gone extinct. I know I have faults, both physical and intellectual, and would not wish them on my (future) children. Part of being a parent is the hope that your children will surpass you, not make the same mistakes you did. I think this may be what allows parenthood the potential to be a selfless, rather than selfish, act.
I think that the Professor may have shared some of my views and chose to participate in the project as she saw no other way to influence the future towards the directions she wished. In the end, she felt this guaranteed that a woman with her values would be in a position of great power after her death, even if she did not necessarily believe in the truth of the reincarnation or agree with the morality of the practice.
The story also ignores the genetic components of personality and intellect, but I suppose cloning is a possibility with modern science.