  We study the Cauchy problem for a general inhomogeneous linear moment partial
differential equation of two complex variables with constant coefficients,
where the inhomogeneity is given by the formal power series. We state
sufficient conditions for the convergence, analytic continuation and
summability of formal power series solutions in terms of properties of the
inhomogeneity. We consider both the summability in one variable t (with
coefficients belonging to some Banach space of Gevrey series with respect to
the second variable z) and the summability in two variables (t,z).
