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By applying a hybrid (kinetic ions and fluid electrons) simulation code, we study the plasma environment of Saturn´s largest moon Titan during Cassini´s T96 flyby on 1 December 2013. The T96 encounter marks the only observed event of the entire Cassini mission where Titan was located in the supersonic solar wind in front of Saturn´s bow shock. Our simulations can quantitatively reproduce the key features of Cassini magnetic field and electron density observations during this encounter. We demonstrate that the large-scale features of Titan´s induced magnetosphere during T96 can be described in terms of a steady state interaction with a high-pressure solar wind flow. About 40 min before the encounter, Cassini observed a rotation of the incident solar wind magnetic field by almost 90°. We provide strong evidence that this rotation left a bundle of fossilized magnetic field lines in Titan´s ionosphere that was subsequently detected by the spacecraft. Fil: Feyerabend, Moritz. Georgia Institute Of Techology; Estados Unidos Fil: Simon, Sven. Georgia Institute Of Techology; Estados Unidos Fil: Neubauer, Fritz M.. Universitat Zu Köln; Alemania Fil: Motschmann, Uwe. Deutsches Zentrum Fur Luft- Und Raumfahrt; Alemania. Technische Universitat Braunschweig; Alemania Fil: Bertucci, Cesar. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina Fil: Edberg, Niklas J. T.. Instiutet For Rymdfysik; Suecia Fil: Hospodarsky, George B.. University Of Iowa; Estados Unidos Fil: Kurth, William S.. University Of Iowa; Estados Unidos