  We describe the kernel of the canonical map from the Floyd boundary of a
relatively hyperbolic group to its Bowditch boundary.
  Using our methods we then prove that a finitely generated group $H$ admitting
a quasi-isometric map $\phi$ into a relatively hyperbolic group $G$ is
relatively hyperbolic with respect to a system of subgroups whose image under
$\phi$ is situated in a uniformly bounded distance from the parabolic subgroups
of $G$.
