The Fifth Circuit issued a published decision holding that a person seeking to adjust status to Permanent Resident who has committed fraud under INA § 212(a)(6) may not adjust status under § 245(i). The applicants in question were seeking to adjust status to permanent resident based on an approved employment-based petition, but had originally entered the U.S. with visas bearing other people's names. This is considered fraud under INA § 212(a)(6). Thus, while the applicants' time out of status might have been waiver under § 245(i) and an illegal entry would have been waived under § 245(i), the fraud committed when entering the U.S. is a separate matter. If the applicants had also been eligible for fraud waivers under INA § 212(i), they might have been able to adjust status in the United States.
In this case, it appears that the applicants were ineligible for fraud waivers under § 212(i). According to the Fifth Circuit's decision, the applicants had a U.S. citizen child, but unfortunately, a fraud waiver is available under § 212(i) only where an applicant for admission has a spouse or parent who is a U.S. citizen or Permanent Resident. The waiver is not available to people who only have a child who is a U.S. citizen or Permanent Resident.