Clearly, this question is an application of Radon-Nikodym theorem. So, I guess all needed to show is $\mu\ll m$, but I have no clue how to show that here. The question also has hint which I struggle to understand. The hint is; let $g_A:y\to \mu(A+y)$ and define $\nu(A\times E)=\int_Eg_A(y)dm(y)$. Why do we should define such another measure? What does it give us?