Is there a term for the continuance of the later editions of a book?

Is there a term, or even a designated subgenre, for the continuance by a substitute author of the later editions of a book after the death of the author? Three example of such continuance:

  • "The Common Sense Book of Baby and Child Care" was originally by Benjamin Spock. Later editions were retitled "Dr Spock's Baby and Child Care", and were revised by Michael Rothenburg, Steven Parker and then Robert Needlman
  • Hints from Heloise
  • The Ludlum thrillers
  • "The elements of style" was originally written by William Strunk Jr, but a later version was expanded by E.B. White

Solution 1:

I would suggest posthumous franchise book. Although not a common term, it is readily understood, and Google indicates it is occasionally used, and in a manner consistent with your request.

The parent term is media franchise which is the development of derivative works of art from an original, typically by someone other than the original author.

Solution 2:

Yes, there is! The term you are looking for is continuation novel.

Wikipedia defines it:

A continuation novel is a novel in the style of an established series, produced by a new author after the original author's death

Continuation novels may be official, produced with the permission of the late author's literary executors, or unofficial where the original author's works are now out of copyright.

History Today wrote on "Picking Up the Torch: The Golden Age of the Continuation Novel" in Mach 2015:

The concept of one novelist ‘writing as’ another, usually to expand or continue a literary franchise, is known as a continuation novel, and is an increasingly familiar feature of the contemporary literary landscape. ...

The continuation novel differs from fan fiction (also enjoying a purple patch, which is unlikely to be a coincidence) chiefly in its ‘official’ nature. The books are commissioned by the deceased author’s estate, written with its approval, and marketed using both author’s brand associations. They are, in a sense, the logical conclusion of the familiar marketing tool of comparing a new author to an established author: ‘For fans of…’ or ‘Author A meets Author B’. The first well-known example of this model of publishing with an established author ‘picking up the torch’ on official business does not occur until the post-war period, when, in 1968, Kingsley Amis wrote Colonel Sun, a ‘new’ James Bond novel under the pseudonym Robert Markham at the behest of Ian Fleming’s estate. Tantalisingly one reviewer of Amis’ book noted that while it was unusual for an established author to continue a franchise in this manner, it was not unprecedented, though my search for an example predating 1968 has proved fruitless thus far. Continuation novels have detractors. ‘The posthumous pseudo-sequel never amounts to more than a nostalgic curiosity’ wrote, ironically, Kingsley’s son Martin Amis in a review of Perchance to Dream, Robert B. Parker’s authorised attempt to resurrect Chandler in 1991.