On a theorem of Scott and Swarup

Let 1 --> H --> G --> Z --> 1 be an exact sequence of hyperbolic groups ind uced by an automorphism phi of the free group H. Let H-1 (subset of H) be a finitely generated distorted subgroup of G. Then there exist N > 0 and a f ree factor K of H such that the conjugacy class of K is preserved by phi(N) and H-1 contains a finite index subgroup of a conjugate of K. This is an a nalog of a theorem of Scott and Swarup for surfaces in hyperbolic 3-manifol ds.