The first game in Paul Keres' book "The Complete Games of Paul Keres" is a correspondence game against "A. Karu" who is otherwise unidentified. I could find no entry for him in Chess Personalia by Jeremy Gaige.
Who was he?
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Investigating a bit further, we find that A. Karu wasn't quite an "ordinary Joe", he was actually one of Estonia's strongest correspondence players at the time.
He finished shared 6.-7. place at the Estonian correspondence chess championship in 1935/36: table.
He lived in the small village of Haaslava, and he took part in a correspondence tournament organized by the Deutsche Schachzeitung: Uus Eesti 16 veebruar 1936.
According to 365chess.com, Aivi Karu was a female player from Estonia.
She has 12 games logged, including those with Keres, and scored 20.83%. In fairness, she played against highly rated players (elo's above 2000), so my guess is that she was an amateur player who played some correspondence, training games and open tournaments where she was inevitably mismatched.
The best sources I can find reference a Aivi Karu, who Keres played in correspondence chess.
Take note (from Wikipedia):
[Keres] played about 500 correspondence games, and at one stage had 150 correspondence games going simultaneously.
It is likely this was a person he played in correspondence, but we may never know who he/she actually was.
Also worthy of note, Keres was only fifteen years old when he played this game!