Mozart wrote these near the end of his life. These are the first and the last of a three part series of quartets supposed to be dedicated to the king of Prussia, Friedrich Wilhelm II. They were never fully paid however, and were also not published by Mozart himself.
They were published posthumously, and the publisher added the dedication. That the dedication is real, is also proven by the prominence of the cello in all three quartets: the king was an avid cello player.
The Amadeus Quartet existed for forty years since 1947. When they started, they promised to disband when one of them died or otherwise left the group. So when in 1987 the violist died, they ceased to exist.
They have always recorded for Deutsche Gramophone, which made their performances well known and critically acclaimed.