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We report on recent results from a test of the Einstein Equivalence Principle, a cornerstone of general relativity, performed by measuring the gravitational redshift with the VLBI spacecraft of the RadioAstron mission. The spacecraft, which orbits Earth in a ~9 d eccentric orbit reaching distances up to the Moon, along with ground stations at Pushchino, Russia and Green Bank, USA, were each equipped with hydrogen maser frequency standards with frequency stability on the order of 10-15. Combining two-way and one-way communication modes in interleaved sessions at 8.4 and 15 GHz between 2015 and 2017, the largest systematics in the redshift measurement can be suppressed, particularly the non-relativistic Doppler shift. Never before has the gravitational redshift been probed with such high accuracy over such large distances near Earth. We also discuss the prospect of reducing the relative uncertainty in our measurements to between 10-4 and 10-5 using VLBI recordings of thespacecraft signal.