Previous studies have shown that there is a correlation between the By component of the interplanetary magnetic field (IMF) and the By component observed in the magnetotail lobe and in the plasma sheet. However, studies of the effect of IMF By on several magnetospheric processes have indicated that the By component in the tail should depend more strongly on the recent history of the IMF By rather than on the simultaneous measurements of the IMF. Estimates of this timescale vary from ∼25 min to ∼4 h. We present a statistical study of how promptly the IMF By component is transferred into the neutral sheet, based on Cluster observations of the neutral sheet from 2001 to 2008, and solar wind data from the OMNI database. Five thousand nine hundred eighty-two neutral sheet crossings during this interval were identified, and starting with the correlation between instantaneous measurements of the IMF and the magnetotail (recently reported by Cao et al. (2014)), we vary the time delay applied to the solar wind data. Our results suggest a bimodal distribution with peaks at ∼1.5 and ∼3 h. The relative strength of each peak appears to be well controlled by the sign of the IMF Bz component with peaks being observed at 1 h of lag time for southward IMF and up to 5 h for northward IMF conditions, and the magnitude of the solar wind velocity with peaks at 2 h of lag time for fast solar wind and 4 h for slow solar wind conditions.