Lempert's stable embedding conjecture for three-dimensional CR manifolds

Let $(X, HX, J)$ be a three dimensional strongly pseudoconvex CR manifold. A stable embedding is a CR embedding $f:(X, HX, J)\rightarrow\mathbb C^k$ such that every sufficiently small deformation of the CR structure admits a nearby embedding into the same $\mathbb C^k$. Assume that $(X, HX, J)$ is the boundary of a Stein manifold. Lempert's stable embedding conjecture. Every CR embedding

$$f:(X, HX, J)\rightarrow\mathbb C^k$$

is stable. Lempert's conjecture concerns whether embeddability is preserved under small deformations of a three-dimensional strongly pseudoconvex CR structure when the original manifold bounds a Stein manifold; the supplied text does not indicate whether it has been resolved.