  The aim of this short note is to present a proof of the existence of an
$A_\infty$-quasi-isomorphism between the $A_\infty$-$\mathrm
S(V^*)$-$\wedge(V)$-bimodule $K$, introduced in \cite{CFFR}, and the Koszul
complex $\mathrm K(V)$ of $\mathrm S(V^*)$, viewed as an $A_\infty$-$\mathrm
S(V^*)$-$\wedge(V)$-bimodule, for $V$ a finite-dimensional (complex or real)
vector space.
