I'm trying to understand the proof for Lemma 4.8 in Lyndon & Schupp Combinatorial Group Theory, page 26, proposition 4.8.
In the very end of this proof, we have: $N \unlhd F$ where $F$ is a finitely generated free group. $[F:N]=p$, $p$ prime. $K \unlhd N$, $K \unlhd F $. $u,v \in N$ such that their images in $N/K$ are not conjugate. It is then claimed that the images of $u,v$ in $F/K$ are not conjugate as well. Why is that?