Analytic solutions of convolution equations on convex sets with a mixed structure. II

We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable neighborhood basis of convex domains. Mentioned conditions are obtained in terms of the boundary behavior of convex univalent functions which are defined by these sets.