"Let $w_1$ and $w_2$ be elements of a free group $F$. Then it is decidable whether there is an automorphism of $F$ carrying $w_1$ into $w_2$."
(R.C.Lyndon, P.E.Schupp, Combinatorial Group Theory, Chapter I, Prop.4.19)
Is this an answer on your question? I think it's hard to get something more specific.