  Inspired by the recent work of Chen-Sti\'enon-Xu on Atiyah classes associated
to inclusions of Lie algebroids, we give a very simple criterium (in terms of
those classes) for relative Poincar\'e-Birkhoff-Witt type results to hold. The
tools we use (e.g. the first infinitesimal neighbourhood Lie algebroid) are
straightforward generalizations of the ones previously developped by Caldararu,
Tu and the author for Lie algebra inclusions.
