Let $e_n$ be the operad of (say, rational) chains of the operad of little n-disks. Consider the natural embedding $e_n\to e_m$, where $n<m$ and $n,m>1$ induced by the embedding $\mathbb{R}^n\to \mathbb{R}^m$. By the formality theorem $e_n$ is quasiisomorphic to its cohomology $H^*(e_n)$, which is an operad resembling the Poisson or the Gerstenhaber operad, that is it is generated by the commutative multiplication and the bracket.

The question is: can we write down an explicit $\infty$-morphism $H^*(e_n)\to H^*(e_m)$ that corresponds to the embedding under the quasiisomorphism mentioned above.