Forster's conjecture on proper holomorphic embeddings of open Riemann surfaces

An open connected Riemann surface is a connected one-dimensional Stein manifold. Forster's conjecture. Every open connected Riemann surface embeds properly holomorphically into $\mathbb{C}^2$. Forster's conjecture is the one-dimensional case of the optimal embedding-dimension problem for Stein manifolds. It was proved by Stensønes and Globevnik in 1995 for every finitely connected planar domain without isolated boundary points, but the supplied context does not state a proof in full generality.