The relation between the Evershed flow and moving magnetic features (MMFs) is studied using high-cadence, simultaneous spectropolarimetric measurements of a sunspot in visible (630.2 nm) and near-infrared (1565 nm) lines. Doppler velocities, magnetograms, and total linear polarization maps are calculated from the observed Stokes profiles. We follow the temporal evolution of two Evershed clouds that move radially outward along the same penumbral filament. Eventually, the clouds cross the visible border of the spot and enter the moat region, where they become MMFs. The flux patch farther from the sunspot has the same polarity of the spot, while the MMF closer to it has opposite polarity and exhibits abnormal circular polarization profiles. Our results provide strong evidence that at least some MMFs are the continuation of the penumbral Evershed flow into the moat. This, in turn, suggests that MMFs are magnetically connected to sunspots.