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A superconducting coupling solenoid mounted around four conventional RF cavities, which produces up to 2.6 T central magnetic field to keep the muons within the cavities, is to be used for the Muon Ionization Cooling Experiment (MICE). The coupling coil made from copper matrix NbTi conductors is the largest of three types of magnets in MICE both in terms of 1.5 m inner diameter and about 13 MJ stored magnetic energy at full operation current of 210 A. The stress induced inside the coil assembly during cool down and magnet charging is relatively high. In order to validate the design method and develop the coil winding technique with inside-wound SC splices required for the coupling coil, a prototype coil made from the same conductor and with the same diameter and thickness but only one-fourth long as the coupling coil was designed and fabricated by ICST. The prototype coil was designed to be charged to strain conditions that are equivalent or greater than would be encountered in the coupling coil. This paper presents detailed design of the prototype coil as well as developed coil winding skills. The analyses on stress in the coil assembly and quench process were carried out.