WASHINGTON, June 23 (Reuters) - The U.S. Supreme Court on Wednesday made it easier for President Joe Biden to remove the head of the federal housing finance agency while also nixing separate claims brought by shareholders of mortgage finance companies Fannie Mae and Freddie Mac. The justices upheld part of a lower court ruling that the Federal Housing Finance Agency’s structure is unconstitutional under the separation of powers doctrine because the agency’s lone director is insufficiently accountable to the president. But the justices faulted the lower court for allowing the shareholders to pursue separate litigation challenging a 2012 agreement between the FHFA and the Treasury Department arising from the government’s rescue of the mortgage finance firms following the 2008 housing crisis. The court sent the case back to lower courts on whether the shareholders can obtain relief based on their constitutional claims. (Reporting by Lawrence Hurley; Editing by Will Dunham) Our Standards: The Thomson Reuters Trust Principles.