Janet writes, "My mother was detained at the airport about six years ago and refused entry into the United States because the officers suspected that she was illegally working (at the time of leaving a few months ago, she was randomly checked and they found several thousand dollars in cash in her bag and that information was entered in the database). She was questioned extensively in a separate room, and under pressure she confessed to illegal employment. In return for not being arrested and prosecuted, she agreed to a voluntary departure and was banned for five years. Her tourist visa was cancelled on the spot and she was deported on the next flight. Now I want to sponsor her for permanent residence and I am wondering if this is going to be a straightforward case of a US citizen sponsoring her parent or it is a lot more complicated and I need to do a lot of additional paperwork."
The good news is that her ban is over and at this point you simply need to file USCIS Form I-130 and making sure that you disclose all the details of her problems at the airport and the ban. Also provide copies of her paperwork. Chances are that if she is otherwise eligible she will be approved but expect her to be questioned about her unlawful employment. Even if she is denied, the worse that can happen at this point is that you lose just the fee that you pay. She cannot be arrested or charged with any crime as long as she is overseas. A denial might also mean that she will not be able to get another B-1 visa either.