On the residual finiteness of generalized free products with cyclic amalgamation

Let $G$ be the free product of residually finite groups $A$ and $B$ with amalgamated cyclic subgroups $H$ and $K$. It is proved that if there exist homomorphisms of the groups $A$ and $B$ onto virtually polycyclic groups which are injective on the subgroups $H$ and $K$ then $G$ is a residually finite group.