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Imaging of the shadow around supermassive black hole (SMBH) horizon with avery long baseline interferometry (VLBI) is recognized recently as a powerfultool for experimental testing of Einstein's General relativity. The EventHorizon Telescope (EHT) has demonstrated that an Earth-extended VLBI with themaximum long base ($D=10,700$ km) can provide a sufficient angular resolution$\theta\sim 20~\mu$as at $\lambda=1.3$ mm ($\nu=230$ GHz) for imaging theshadow around SMBH located in the galaxy M87$^\ast$. However, the accuracy ofcritically important characteristics, such as the asymmetry of thecrescent-shaped bright structure around the shadow and the sharpness of atransition zone between the shadow floor and the bright crescent silhouette,both of order $\Delta\theta\sim 4~\mu$as, is still to be improved. In ourprevious paper we have shown that Space-Earth VLBI observation within a jointMillimetron and EHT configuration at the near-Earth high elliptical orbit (HEO)can considerably improve the image quality. Even more solid grounds for firmexperimental validation of General relativity can be obtained with a higherresolution available within the joint Millimetron and EHT program at theLagrangian point L2 in the Sun-Earth system with an expected imaging resolutionat 230~GHz of $\Delta\theta\sim 5~\mu$as. In this paper we argue that in spiteof limitations of L2 orbit, an adequate sparse $(u,v)$ coverage can be achievedand the imaging of the shadows around Sgr A$^\ast$ and M87$^\ast$ can beperformed with a reasonable quality.

High Resolution Imaging of a Black Hole Shadow with Millimetron Orbit around Lagrange Point L2