A two-player differential game is considered where a spy infiltrates the region of interest and a defender pursues and tries to capture the spy before it leaves such region. This letter provides the complete solution of this game by characterizing the Barrier surface which separates the state space into the regions of win of the defender and the spy. In each region the optimal strategies that guarantee the prescribed outcome are provided. This is in contrast to recent results addressing the same problem where the proposed strategies do not guarantee capture of the spy by the defender when initially this outcome was prescribed by the game of kind solution.