First, she's not going to get a green card or citizenship. A person does not get a green card or citizenship automatically or quickly through marriage. It's a very involved process to get the green card, taking many years, if not a lifetime. Applicants are investigated more thoroughly than murder suspects are. It's no longer possible to get citizenship through marriage at all; a married person seeking citizenship simply has to live in the U.S. with the green card for the required number of years to be able to get citizenship without using the marriage.
Second, while it is technically not illegal to marry her, it is extremely illegal to lie to the government about the reasons for the marriage, which you would have to do, because if the government finds out that her main gain was a green card or citizenship, then she won't get either. She'd have a better chance if she stayed unmarried. If the government finds out that someone's reason for marriage was to get a green card or citizenship, then the person will be banned from even visiting the country.