Perturbations of surjective convolution operators

Let $\mu_1$ and $\mu_2$ be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator $f\, \rightarrow \, \mu_1 * f$ is surjective when it acts on a space of functions or (ultra)distribu- tions, and we investigate whether the perturbed convolution operator $f\rightarrow$ $(\mu_1 + \mu_2)* f$ is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.