  We investigate vertical isomorphisms of Fedosov dg manifolds associated with
a Lie pair $(L,A)$, i.e. a pair of a Lie algebroid $L$ and a Lie subalgebroid
$A$ of $L$. The construction of Fedosov dg manifolds involves a choice of a
splitting and a connection. We prove that, given any two choices of a splitting
and a connection, there exists a unique vertical isomorphism, determined by an
iteration formula, between the two associated Fedosov dg manifolds. As an
application, we provide an explicit formula for the map
$\mathrm{pbw}_2^{-1}\circ \mathrm{pbw}_1$ associated with two
Poincar\'{e}--Birkhoff--Witt isomorphisms that arise from two choices of a
splitting and a connection.
