  Let $A$ and $B$ be two Morita equivalent finite dimensional associative
algebras over a field $\Bbbk$. It is well known that Hochschild cohomology is
invariant under Morita equivalence. Since infinitesimal deformations are
connected with the second Hochschild cohomology group, we explicitly describe
the transfer map connecting $\mathsf{HH}^2(A)$ with $\mathsf{HH}^2(B)$. This
allows us to transfer Morita equivalence between $A$ and $B$ to that between
infinitesimal deformations of them. As an application, when $\Bbbk$ is
algebraically closed, we consider the quotient path algebra associated to $A$
and describe the presentation by quiver and relations of the infinitesimal
deformations of $A$.
