But napisze and napiszę are pronounced the same, so napiszę should also be accepted, with the translation "I will never write..." Or is their no way to handle an ambiguity of this sort in Duolingo?
They are not pronounced completely the same by most of people but TTS pronounces both in the same way.
I just got this as a listening exercise as well. I also answered it with "napiszę" and got it wrong.
That's very strange, audio exercises are blocked. But then we also know of sentences that were deleted but still appear sometimes...
Unfortunately, we cannot do anything more about it. We cannot accept "napiszę", because it would then be accepted as a translation of "He will never write", and that would be obviously wrong...
How do you know it is she? Oh yes, it could be he or she will never write this book.