Promoting and Respecting Economically Vital American Innovation Leadership Act or the PREVAIL Act This bill addresses various issues relating to the U.S. Patent and Trademark Office (PTO), including by imposing additional requirements on administrative patent validity challenges (proceedings to review and potentially cancel issued patents) at the PTO. The bill modifies provisions relating to inter partes reviews (IPRs) and other administrative patent validity proceedings, including by prohibiting an administrative patent judge who participated in deciding whether to institute an IPR (i.e., whether to allow the IPR to proceed based on the initial petition) from also participating in deciding the final outcome of the same IPR; prohibiting a person (individual or entity) from petitioning for an IPR against a patent unless the person has been sued for or charged with infringing that patent, whereas currently any person may petition for an IPR; prohibiting a person who has challenged a patent's validity in an IPR from raising the same challenges against the patent in other proceedings (e.g., district court) if the IPR has been instituted; and raising the burden that the petitioner in an IPR must meet to invalidate a previously-issued patent claim. This bill also makes institutions of higher education (IHEs) and nonprofit entities that hold patents on behalf of IHEs eligible for reduced patent-related fees, including filing fees. (Currently, employees of IHEs are eligible for reduced fees but not the IHEs themselves.) The bill also makes fees collected by the PTO available for the PTO's use without further appropriations from Congress, whereas currently some of the collected fees are subject to appropriations.