Mea Culpa if this has been asked (I did a search, but nothing jumped out), but why the difference?
Hawking uses it in his A Brief History of Time .
Thanks
Q
For the opening section of the book?? Odd.
From a dictionary website:
So it is a real word, and could arguably apply to the introduction to a book; but that would be a very bad choice, IMO, when we have a more exact one in “foreword”. The use of “foreward” in that context, whenever you see it, was probably not a choice at all but a mistake or misprint.
This is a guess, but it might be a sly intentional misprint that alludes to the foreward progress of time.
Maybe he thought it was a clever play on words (combining foreword/forward)?
I don’t, but maybe he did. 
I have noticed this in other works as well, not just his.
Maybe it’s a British “Thang”, and we wouldn’t understand? 
Q