This meant that the principality was seen as inherited by his closest cognate relative on the basis of the testament of Frederic-Henry , Frederick I of Prussia . He handed over the principality 's lands but not the title to France in 1713 . Because William III died without legitimate children , the principality was regarded as having been inherited by his closest cognate relative on the basis of the testament of Frederic-Henry , Frederick I of Prussia , who ceded the principality -- at least the lands , but not the formal title -- to France in 1713 .