The part that covers the years 1459-1486 was written in April 1486 (after Henry Tudor had become Henry VII of England) by someone who had been an insider at the court of Richard III—someone described in it as being a doctor of canon law and member of Edward IV's council. Some historians believe that author was John Russell, Bishop of Lincoln, who was Richard's Chancellor for most of his reign (until Richard fired him on 24 July 1485) but who now wanted to please the new king Henry.
Over the years, there has been confusion between the "second" and "third" continuators, and the "fourth" continuator claims not to know the identity of the third. It is, in fact, the second continuator (covering the period 1459-1486) who claims to be writing in April 1486, and, sure enough, this section ends with the marriage of Henry VII of England and Elizabeth of York and the rebellion that followed. This date ties in with the survival of a copy of Titulus Regius in the text, and Russell is known to have been at Crowland during April, 1486.