Completing the unfinished work of a great master is a very delicate task. In my opinion it can honestly be undertaken only if the original fragment contains all of the main ideas of the unfinished work. In such a case a respectful craftsman may attempt, after an absorbing study of the master’s style, to elaborate on those ideas in a way which to the best of his knowledge might have been the way of the master himself. The work in question will probably have analogies among other, completed works of the master, and careful investigation of his methods in similar situations will indicate possible solutions of the problems posed by the unfinished work. Even then the artist who goes about the ticklish task will feel slightly uneasy, knowing from his own experience as a composer that the creative mind does not always follow its own precedents. He is more conscious of the fact that unpredictability is one of the most jealously guarded prerogatives of genius. … However, scruples of this kind may be set aside once we are certain that the author of the fragment has put forth the essential thematic material that was expected to go into the work. If this is not the case, I feel that no one, not even the greatest genius, should dare to complete the fragments left by another genius.”

exploration of Schubert’s music, I’ve come to realize that I don’t quite put a lot of faith in works completed by someone other than the composer. To me, it feels…. spurious, apocryphal, dare I say even counterfeit.

1. In my opinion it can honestly be undertaken only if the original fragment contains all of the main ideas of the unfinished work. In such a case a respectful craftsman may attempt, after an absorbing study of the master’s style, to elaborate on those ideas in a way which to the best of his knowledge might have been the way of the master himself.  – Agreed. Lots. While things like orchestration and tempi and the finer points of an unfinished piece can probably be extrapolated from the style of the period and more specifically of that of the composer, something as open-ended as actually writing a theme (or even developing it) is nearly impossible to say. It’s like the difference between being given the choice between two options as opposed to predicting the exact outcome of a long series of events. It is not a multiple choice question, nor is it one that an educated guess could solve. 
2. Even then the artist who goes about the ticklish task will feel slightly uneasy, knowing from his own experience as a composer that the creative mind does not always follow its own precedents. He is more conscious of the fact that unpredictability is one of the most jealously guarded prerogatives of genius- I love that part about unpredictability and genius. I suppose this is related to the first. In my post on Berg’s piano sonata I talked about the serendipitous nature of a piece of music and how any number of factors could have forever changed the direction of a piece of work, thereby meaning that the piece, as it exists, is more like a snapshot of things (the composer’s life, emotions, viewpoint, gastrointestinal condition, etc.), not necessarily as they were upon writing the piece, but upon finishing it, and thus if not put on paper and kept forever, would be extremely evanescent. How much more so is this the case with trying to pick up where another composer left off, and, as the case may be, trying to (or claiming to) read their mind?
3. If this is not the case, I feel that no one, not even the greatest genius, should dare to complete the fragments left by another genius. – And finally, the real point here. If you want to take credit for writing a piece based on something someone else wrote, then write “Variations on a theme of…” or something. Why would anyone really want to do that anyway? Krenek edited a few movements of Mahler’s unfinished tenth symphony at Alma’s behest, but went no further. Is it just that someone wanted to hear what the completed piece could have sounded like? Or was it that you can’t sell or perform an incomplete piece of music? Who knows? 

As an example, Krenek explains that a careful student of Rembrandt’s style might be able to complete a painting lacking one or two corners but could never supply two entirely missing paintings from a four-painting series; such an attempt would result only in “more or less successful fakes.” Turning to a musical example, Krenek, evidently unaware of the surviving sketch of a third movement, avers that Schubert’s own “Unfinished” Symphony “was left by its creator with only two of its four movements written; of the other two there is no trace. It would be possible to write two or more movements to the symphony in the manner of Schubert, but it would not be Schubert.”