- We study in some detail the properties of the mathematically correct formulation of the classical Einstein-Rosen "bridge" as proposed in the original 1935 paper, which was shown in a series of previous papers of ours to represent the simplest example of a static spherically symmetric traversable lightlike thin-shell wormhole. Thus, the original Einstein-Rosen "bridge" is not equivalent to the concept of the dynamical and non-traversable Schwarzschild wormhole, also called "Einstein-Rosen bridge" in modern textbooks on general relativity. The original Einstein-Rosen "bridge" requires the presence of a special kind of "exotic" matter source located on its throat which was shown to be the simplest member of the previously introduced by us class of lightlike membranes. We introduce and exploit the Kruskal-Penrose description of the original Einstein-Rosen "bridge". In particular, we explicitly construct closed timelike geodesics on the pertinent Kruskal-Penrose manifold.