If the application is approved, the applicant's permanent residence shall be recorded as of the date of the order approving the adjustment of status. An application for adjustment of status, as a preference alien, shall not be approved until an immigrant visa number has been allocated by the Department of State, except when the applicant has established eligibility for the benefits of Public Law 101-238. No appeal lies from the denial of an application by the director, but the applicant, if not an arriving alien, retains the right to renew his or her application in proceedings under 8 CFR part 240. [Emphasis added]