Connectedness conjecture for the source fibers of presymplectic groupoids

Let $G$ be a presymplectic manifold, and let $s,t:G\to M$ be smooth surjective submersions onto a smooth manifold $M$ whose fibers are presymplectic orthogonal. A Poisson structure on $M$ is obtained from the presymplectic structure on $G$ as in Liberman's lemma.

Connectedness conjecture. Theorem 1 holds also when the $s$-fibers are not connected.

The conjecture proposes that the connectedness hypothesis in the construction of the induced Poisson structure can be removed; the source does not provide a resolution.