Long-duration gamma-ray bursts (GRBs) are thought to come from the core-collapse of Wolf-Rayet stars. Whereas their stellar masses $M_*$ have a rather narrow distribution, the population of GRBs is very diverse, with gamma-ray luminosities $L_gamma$ spanning several orders of magnitude. This suggests the existence of a hidden stellar variable whose burst-to-burst variation leads to a spread in $L_gamma$. Whatever this hidden variable is, its variation should not noticeably affect the shape of GRB lightcurves, which display a constant luminosity (in a time-average sense) followed by a sharp drop at the end of the burst seen with Swift/XRT. We argue that such a hidden variable is progenitor stars large-scale magnetic flux. Shortly after the core collapse, most of stellar magnetic flux accumulates near the black hole (BH) and remains there. The flux extracts BH rotational energy and powers jets of roughly a constant luminosity, $L_j$. However, once BH mass accretion rate $dot M$ falls below $sim L_j/c^2$, the flux becomes dynamically important and diffuses outwards, with the jet luminosity set by the rapidly declining mass accretion rate, $L_jsim dot M c^2$. This provides a potential explanation for the sharp end of GRBs and the universal shape of their lightcurves. During the GRB, gas infall translates spatial variation of stellar magnetic flux into temporal variation of $L_j$. We make use of the deviations from constancy in $L_j$ to perform stellar magnetic flux tomography. Using this method, we infer the presence of magnetised tori in the outer layers of progenitor stars for GRB 920513 and GRB 940210.
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