TITLE: One-ended finitely presented subgroups of hyperbolic groups
QUESTION [6 upvotes]: 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?

REPLY [9 votes]: There is a proof of this theorem due to Thomas Delzant:
T. Delzant, L’image d’un groupe dans un groupe hyperbolique, Comment. Math. Helv.
70 (1995), no. 2, 267–284.
There is also a version for relatively hyperbolic groups du to Francois Dahmani:
Accidental Parabolics and Relatively Hyperbolic Groups, Israel Journal of Mathematics, Volume 153, Issue 1, pp 93–127