Federal Funding Accountability for Sexual Harassers Act This bill requires institutions of higher education (IHEs) that receive federal funding to report certain instances of discrimination on the basis of sex. Such IHEs must report, to all federal agencies that awarded competitive research and development grants over the previous 10 years and to the Federal Audit Clearinghouse, substantiated findings of discrimination (including harassment) on the basis of sex by a principal investigator or program director. A principal investigator or program director is an individual designated to direct or lead a project, program, or activity supported by a federal grant and who is responsible and accountable for the proper conduct of the project, program, or activity. In addition, each federal department or agency that is authorized to award competitive research and development grants must take into consideration any such reports when making the final decision of whether to award a grant to an IHE. The department or agency may condition the grant award on the prohibition of an individual for whom a report has been filed from using the grant award or carrying out activities under the grant. The National Academies of Sciences, Engineering, and Medicine must study and report on the implementation and effectiveness of strategies employed to address and prevent sexual harassment.