I liked the novel, but the whole setup is written under an inaccurate understanding of how the Centauri system is arranged. Proxima is a long way out from Alpha Centauri A and B (0.21 light years), orbiting their mutual center of mass, and A and B themselves are a fair distance apart (from 11.2 to 35.6 AU). Any of the three stars could have planets in close stable orbits; we already know Proxima has one.

ETA: Actually, we know of another one around B.

https://en.wikipedia.org/wiki/Alpha_Centauri#Planets