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We report on the recent results of testing one of the aspects of Einstein's principle of equivalence - the effect of gravitational redshift, by means of its precision measurement using the Spectr-R as part of the VLBI mission Radioastron. The spacecraft, which orbits Earth in a ~9 d eccentric orbit, along with ground stations at Pushchino, Russia and Green Bank, USA, were each equipped with high stability hydrogen maser frequency standards. To compensate for non-relativistic effects, we used a combination of one way and two way operating modes. We report success in updating the clock offset value by re-processing the accumulated data from 5% to 15%. This makes it possible to bring the error of correspondence of the measured gravitational shift to the calculation formula of general relativity to the level of 10-3. It should be noted that never before has the gravitational redshift been measured with such accuracy at such large distances from the Earth of 350,000 km.