Then you'd need to fake the handwriting on the new envelope too. Which is certainly could be done by Soviet security apparatus: they could even write the whole

Then you'd need to fake the handwriting on the new envelope too. Which is certainly could be done by Soviet security apparatus: they could even write the whole letter, or even make you write the letter they want really. But it's a lot more bureaucratically involved and requires totally different set of skills than what a minder at postal exchange has.