In *Hyperbolic groups* (page 82), Gromov claims that, by a standard application of Thurston's method of *geodesic (hyperbolic) simplices*, it can be prove that a hyperbolic group contains finitely many pairwise non conjugate subgroups isomorphic to a fixed one-ended finitely presented group.

I took a look on the usual references dealing with hyperbolic groups, but I didn't find any details. Do you know references about this result and/or Thurston's method?