The free multiplicative Lie algebra $L(P)$ for a finitely generated parafree group $P$

Let $P$ be a group, $L(P)$ be the free multiplicative Lie algebra with normal subgroup $Γ_n(P)$ generated by Lie bracket ``commutators'' of weight $n$ and $\{ γ_n(P) \}$ be the lower central series of $P$. We prove that $Γ_n(P) \simeq γ_n(P)$ for arbitrary $n \geq 1$ and $P$ a finitely generated par