  Let $X$ be a Godeaux surface over $\mathbb{C}$ and $q_{X}\colon Y\to X$ be
its universal cover. We show that the pullback map $q^{*}_{X}\colon Br(X)\to
Br(Y)$ is injective if $\rho(Y)=9$. Our arguments rely on a degeneration
technique that also applies to other examples.
