In this paper we continue to study small amplitude solutions of the damped
cubic NLS equation, driven by a random force (the study was initiated in our
previous work [A.Dymov, S.Kuksin, Comm. Math. Phys.’2021] and continued in
[A.Dymov, S.Kuksin, A.Maiocchi, S.Vladuts, arXiv:2104.11967]). We write
solutions of the equation as formal series in the amplitude and discuss the
behaviour of this series under the wave turbulence limit, when the amplitude
goes to zero, while the space-period goes to infinity.