This question asks about the phases of a hypothetical moon of Proxima Centauri b.

What phases of a moon orbiting Proxima Centauri b could be seen?

And In my answer I suggest that Proxima Centauri b can't still have any moon it might have had soon after it formed, unless tidal interactions had not pushed that moon out beyond the true region of stability of Proxima Centauri b.

I suggest that a moon of Proxima Centauri b which formed with the same mass as Earth's Moon and orbiting at the same distance from Proxima Centauri b as the Moon from Earth would have been pushed beyond the true region of stability of Proxima Centauri b by now.

So can anyone calculate the ranges for the mass and orbit of a moon still retained within the region of true stability of Proxima Centauri b?