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The phase I LHC upgrade foresees the installation of a new final focusing for the high luminosity experiences in order to be able to focus the beams in the interaction points to ??* ~0.25 cm. Key element of this upgrade is a large bore (120 mm) superconducting quadrupole. This article proposes a magnet design that will make use of the LHC main dipole superconducting cable. Due to the schedule constraints and to the budget restrictions, it is mandatory to integrate in the design the maximum number of features successfully used during the LHC construction. This paper presents this design option and the rationales behind the several technical choices.