I don’t think that he can. His name isn’t on it. I think OP should be very, very careful about claiming to have written something that doesn’t list him as an author.
Whippymop: I think this is the best suggestion yet. I think I’ll apply using that phrasing.
Will you be telling your professor this is what you’re doing? You don’t want them finding out from the grants’ office.
I agree with others about really thinking through what your long-term goals are before you move forward. If your plan is to attend an elite grad school then you’re in an excellent position to be competitive. Stay where you are, develop your research skills, and make contacts. Even if you’re successful in transferring it doesn’t mean you’ll have the opportunity to do research. And if you’re rejected from these schools a second time you may end up not doing research at your current university either.