The LUCI (LBT Utility Camera in the Infrared) instruments are a pair of near infrared (NIR) imagers and spectrographs for the Large Binocular Telescope (LBT) that include a set of cryogenic exchangeable focal plane masks. Although LUCI covers the NIR zJHK bands at different resolutions with existing gratings, it is not currently possible to get zJHK in a single exposure with a single LUCI which is required for some planetary science programs. To produce a simultaneous zJHK spectrum with a single LUCI, we designed a system consisting of small and simple optical elements to fit within the limited space in the focal plane mask frame to cross-disperse fixed short slits. This system, called MOBIUS (Mask-Oriented Breadboard Implementation for Unscrambling Spectra), consists of a double-folding mirror, a collimating spherical mirror with 180 mm radius of curvature, and a dispersing prism with the rear surface mirror-coated. MOBIUS disperses the input slit perpendicular to the dispersion direction of the gratings in LUCI. The resulting order separation is at least ∼2.7 arcsecond, allowing a slit length of up to ∼2.3 arcsec without mixing orders at the LUCI image plane. Since MOBIUS would be introduced into the existing light path via the exchangeable slit mask mechanism, no modification to the current LUCI instrument is needed. Eventually, binocular observations combining one of the Multi-Object Double Spectrographs (MODS) with LUCI+MOBIUS at the LBT will provide simultaneous coverage from 0.3 to 2.4 μm for studies of asteroids and other faint solar system bodies.