  In this paper, we show that the class of all properly 3-realizable groups is
closed under amalgamated free products (and HNN-extensions) over finite groups.
We recall that $G$ is said to be properly 3-realizable if there exists a
compact 2-polyhedron $K$ with $\pi_1(K) \cong G$ and whose universal cover
$\tilde{K}$ has the proper homotopy type of a 3-manifold (with boundary).
