The integrability converse for Lie algebroid foliations

Let $\mathfrak{g}\to X$ be a Lie algebroid. A simple foliation is the foliation associated to a map from the pair groupoid of a manifold to a Lie groupoid; an LA-groupoid is a Lie algebroid object in Lie groupoids.

Integrability converse. The Lie algebroid $\mathfrak{g}\to X$ is integrable if and only if it is equivalent, as an LA-groupoid, to a simple foliation.

This is proposed as a converse to the result that an integrable Lie algebroid determines a foliation of its base. The statement relates integrability to the classification of simple foliations and remains conjectural in the source.