It's a sentence fragment and, technically, ungrammatical.
However, sentence fragments can still be an arguably acceptable form of stylistic writing: It was simply the best thing in the world. The. Best. (A poor example of good usage, I grant you.)
In your example, the use of a separate "sentence" gives it the same pacing as a long pause in speech, putting emphasis on the fragment and giving it a particular emotional tenor. This is a type of pause that wouldn't be the same with other formatting.
A more explicit example of this (that exaggerates the pacing) could be:
After the winter finished, Eric had to sit on the beach on weekends and attempt school work. While his father talked to all the beautiful women. While he had to look at a book.
Rephrasing to avoid the sentence fragment, while correcting the grammar, would change the pacing and emphasis.
Looking at what you are actually editing, it doesn't appear to me that the fragment is an intentional literary device, but it's best to ask the author—at least with respect to one of the several instances you're seeing. Is it a deliberately used style or an unintentional mistake? Before just changing it to make it grammatical, you should find out what the intent was.
If the author does say it was intentional, and wants to keep it, then you could ask at the Writing site if there are ways of making it seem more deliberate and appropriate.