On embeddings of some quotient algebras of free sums of Lie algebras

Let $(B_i)_{i\in I}$ be a set of Lie algebras; let $X$ be a free Lie algebra; let $F=\Bigl(\,\mathop{\sum\limits_{i\in I}}\nolimits^{*}B_i\Bigr)*X$ be their free sum; let $R$ be an ideal of $F$ such that $R\cap B_i=1$ ($i\in I$); let $V$ be a variety of Lie algebras such that $\mathbf{V}(R)$ is an ideal of $F$. Under some restrictions, we construct an embedding of $F/\mathbf{V}(R)$ into the verbal wreath product of a free algebra of the variety $V$ with $F/R$.