Prompt Approval of Safe Generic Drugs Act This bill authorizes the Food and Drug Administration (FDA) to approve certain applications to market a drug even if the drug's labeling lacks certain safety information. Specifically, an abbreviated application for approval of a generic drug shall not be ineligible for approval solely because the drug's labeling omits safety information that is protected under another drug's exclusivity protections. Similarly, a drug that is approved under this bill shall not be considered mislabeled for lacking such safety information. Generally, an abbreviated application, for the purposes of this bill, is one that (1) uses required information from studies not conducted by the applicant; or (2) seeks approval of a drug that is, for drug approval purposes, a duplicate of an already-approved drug. For any drug approved under this bill, the FDA shall require the drug's labeling to include any safety information that is necessary to assure safe use.