  Given any pair $(L,A)$ of Lie algebroids, we construct a differential graded
manifold $(L[1]\oplus L/A,Q)$, which we call Fedosov dg manifold. We prove that
the cohomological vector field $Q$ constructed on $L[1]\oplus L/A$ by the
Fedosov iteration method arises as a byproduct of the
Poincar\'e--Birkhoff--Witt map established in arXiv:1408.2903. Finally, using
the homological perturbation lemma, we establish a quasi-isomorphism of
Dolgushev--Fedosov type: the differential graded algebras of functions on the
dg manifolds $(A[1],d_A)$ and $(L[1]\oplus L/A,Q)$ are homotopy equivalent.
