Lee's conjecture on global pseudo-Einstein structures

Let $M$ be a closed, strictly pseudoconvex CR $(2n+1)$-manifold with vanishing first Chern class

$$c_1(T_{1,0}M)=0,$$

where $n\geq 2$. A pseudo-Einstein structure is a contact structure whose pseudohermitian Ricci curvature tensor is function-proportional to its Levi metric. Lee's conjecture. The manifold $M$ admits a global pseudo-Einstein structure. The paper invokes this conjecture in the setting of vanishing first Chern class; the supplied text gives no resolution status.