  Let $\mathbf{k}$ be a field of arbitrary characteristic, and let $\Lambda$ be
a finite dimensional $\mathbf{k}$-algebra. In this short note we prove that if
$V$ is a finitely generated strongly Gorenstein-projective left
$\Lambda$-module whose stable endomorphism ring
$\underline{\mathrm{End}}_{\Lambda}(V)$ is isomorphic to $\mathbf{k}$, then $V$
has an universal deformation ring $R(\Lambda,V)$ isomorphic to the ring of dual
numbers $\mathbf{k}[\epsilon]$ with $\epsilon^2=0$. As a consequence, we obtain
the following result. Assume that $Q$ is a finite connected acyclic quiver, let
$\mathbf{k} Q$ be the corresponding path algebra and let $\Lambda = \mathbf{k}
Q[\epsilon] = \mathbf{k} Q\otimes_{\mathbf{k}} \mathbf{k}[\epsilon]$. If $V$ is
a finitely generated Gorenstein-projective left $\Lambda$-module with
$\underline{\mathrm{End}}_{\Lambda}(V)=\mathbf{k}$, then $V$ has an universal
deformation ring $R(\Lambda,V)$ isomorphic to $\mathbf{k}[\epsilon]
