It is not clear from any of your sentences, that the woman has died.
Which are correct:
1) She left us a parting gift of her most wonderful novel.
2) She left us the parting gift of her most wonderful novel.
3) She left us a gift of her most wonderful novel.
4) She left us the gift of her most wonderful novel.
The parting gift/the gift itself is the novel. The novel is the gift. She has passed away but she has left us her final work, which is her most wonderful novel, as a parting gift/gift.
Thank you very much, Mike,
Yes. I understand. That was a hypothetical context I made up. In the ones with 'parting' it is clear that she has 'left' in one way or another. But none of the sentences makes it clear that she has passed away. My apologies for creating needless confusion.
Are the sentences with 'a gift' and 'a parting gift' correct? I thought in these cases one needed 'the gift' and 'the parting gift'.