I don't think there is a program or browser add-on. I have seen some forums where one can program using Chess.com API using Python programming language. Unfortunately, I have a very limited knowledge of the API and how to work with it (and also if it is open-source or not).
automatically download PGN after a Game
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Is there a way (Program or Browser add-on) that can automatically download the PGN file after a game, so you don't have to do it by hand?