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[en] A superconducting transverse gradient undulator (TGU) for the laser wakefield accelerator (LWFA) in Jena, Germany, has been designed and constructed. The transverse magnetic flux density gradient is achieved through a cylindric shape of the undulator halves. The 40-period undulator is designed for a relative energy acceptance of ± 10% around a given central energy, covering both the width and the shot to shot fluctuations of the electron energy spectrum generated by the LWFA at a moderate dispersion of ∝ 20 mm. In this contribution we present details of the technical design and construction of the device and show results of the performed quench tests and field mappings.