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Jets often have a helical structure containing ejected plasma that is both hot and also cooler and denser than the corona. Various mechanisms have been proposed to explain how jets are primarily attributed to a magnetic reconnection between the emergence of magnetic flux and environment or that of twisted photospheric motions that bring the system into a state of instability. Multi-wavelength observations of a twisted jet observed with AIA and IRIS were used to understand how the twist was injected into the jet. We followed the magnetic history of the active region based on the analysis of HMI vector magnetic field computed with the UNNOFIT code. This region is the result of the collapse of two emerging magnetic fluxes (EMFs) overlaid by arch filament systems that have been well-observed with AIA, IRIS, and NVST in H-alpha. In the magnetic field maps, we found evidence of the pattern of a long sigmoidal flux rope (FR) along the polarity inversion line between the two EMFs, which is the site of the reconnection. Before the jet, an extension of the FR was present and a part of it was detached and formed a small bipole with a bald patch (BP) region, which dynamically became an X-current sheet over the dome of one EMF where the reconnection took place. At the time of the reconnection, the Mg II spectra exhibited a strong extension of the blue wing that is decreasing over a distance of 10 Mm (from -300 km/s to a few km/s). This is the signature of the transfer of the twist to the jet. A comparison with numerical magnetohydrodynamics (MHD) simulations confirms the existence of the long FR. We conjecture that there is a transfer of twist to the jet during the extension of the FR to the reconnection site without FR eruption. There connection would start in the low atmosphere in the BP reconnection region and extend at an X-point along the current sheet formed above.