"When Paul visited Moscow in May 2003, to perform a concert in Red Square, he had an audience with President Putin, who told him that hearing the Beatles as a boy growing up in the Soviet Union..."

"... was 'like a gulp of freedom.' On the same visit, former president Gorbachev told Paul: 'I do believe the music of the Beatles taught the young people of the Soviet Union that there is another life.'"

From Craig Brown's "150 Glimpses of the Beatles." 

Also:

Mikhail Safonov was a schoolboy in Leningrad when Soviet radio played ‘A Hard Day’s Night’ as an example of a capitalist song about the relentless pursuit of money.... but before the end of 1965 he had become caught up in a particularly perilous form of Beatlemania. He and his school friends would copy Beatles records and exchange them on the black market. All over the Soviet Union, young fans like Mikhail would write out Beatle lyrics and pass them around, learning English from them. The most rebellious liked to switch the names of Lenin and Lennon, even though discovery could cost them any hope of further education. One school staged and broadcast a show trial of the Beatles, with a prosecutor railing against them as ‘Bugs’. At the end of the trial they were found guilty, in their absence, of antisocial behaviour. But this verdict was set to backfire: ‘The more the state persecuted the Beatles,’ recalls Mikhail, ‘the more they exposed the falsehood and hypocrisy of Soviet ideology. And in attacking something the whole world had fallen in love with, they isolated themselves even more. It made us more doubtful that our beloved country was right after all.’ 

Mikhail’s nickname at school was ‘Ringo,’ because he aped his hairstyle. Having won a silver medal at school, he was obliged to go to the Palace of Culture to collect it, his banned Beatle hair glued down and parted with sugar and water to replicate an approved cut. But as he was leaving, a group of policemen spotted its true length and chastised him for being a long-haired deviant, setting him free only after he had shown them his silver medal. 

As an adult, Mikhail became a senior researcher at the Institute of Russian History in St Petersburg. Looking back, he believes that ‘Beatlemania washed away the foundations of Soviet society … One could argue they did more for the destruction of totalitarianism in the USSR than Solzhenitsyn and Sakharov.’