You might think of it this way: They are not trying to disrespect the author; they are trying to continue a popular series with many fans behind it, and despite the original author not being able to continue it. If the author did not forbid it in their will, I would not assume they would be against the idea of another author continuing their work. And I think it can be done in the spirit of the content, and without disrespect to the author.
There are many series that have been written by multiple authors over the years, not to mention conversion of those works to other media (such as movies). I do not consider all of those works that came after the initial author's demise to be disrespectful or inappropriate, and I think we'd be worse as a society to have lost many of them.