  In this paper we describe finitely generated groups $H$ universally
equivalent (with constants from $G$ in the language) to a given torsion-free
relatively hyperbolic group $G$ with free abelian parabolics. It turns out
that, as in the free group case, the group $H$ embeds into the Lyndon's
completion $G^{\mathbb{Z}[t]}$ of the group $G$, or, equivalently, $H$ embeds
into a group obtained from $G$ by finitely many extensions of centralizers.
Conversely, every subgroup of $G^{\mathbb{Z}[t]}$ containing $G$ is universally
equivalent to $G$. Since finitely generated groups universally equivalent to
$G$ are precisely the finitely generated groups discriminated by $G$ the result
above gives a description of finitely generated groups discriminated by $G$.
