Homotopy braces formality

We show how to extend M. Kontsevich's formality morphism in
Deformation Quantization to a homotopy braces, and hence also a
homotopy Gerstenhaber morphism.
Furthermore it can be seen that M. Kontsevich's and D. Tamarkin's
formality morphisms are homotopic, if in the construction of the
latter one uses the solution of the Deligne conjecture via the
formality morphism of the little disks operad associated to the
Alekseev-Torossian (Drinfeld) associator.