Al-Adli does, in his book Kitab ash-Shatranj (The Book of Chess), but this is the most popular because the faras (horse, the Western knight), rukh (chariot, the Western rook) , and shah (king) all move in the same way in shatranj as they do in regular chess. The firz moves exactly one square diagonally, and was replaced by the queen in Western chess. The alfil (elephant) moves two squares diagonally, jumping over the intervening square, and baydak move like pawns, but with the exception that they are not allowed to move two squares at the outset. When one reaches the back, it's promoted to a firz.
I'm not sure if the Kitab has been translated. Maybe after I work on my Arabic some more, I could do so.