By the way, it says that drafts will save only your words, so presumably not someone's quote included that you're replying to.
However, once loaded back onto the submit screen, minus the quote, you can scroll down and find the original poster's post in the Topic Review box. Clicking the "quote" button will bring it up into your draft, not at the beginning but wherever your typing cursor was sitting.
I hope that makes sense. I used to think that if you wanted to quote someone you had to start by quoting them, but not so as it can be introduced anytime into your reply box.