Realistically, could you build a useful built in closet in a space that is 77.5in x 9.4in?
That is a very shallow space. I think you'd need at least a couple of inches for your doors / front wall, so you're looking at less than 8" deep for the final closet.

You might be better off just installing built-in shelving and/or hooks on that part of the wall to serve as storage space. You could make the shelves 8" deep and then put a sheer curtain over it, if you want to avoid looking at it.