We present a Hubble Space Telescope/Wide Field Planetary Camera 2 weak-lensing study of A520, where a previous analysis of ground-based data suggested the presence of a dark mass concentration. We map the complex mass structure in much greater detail leveraging more than a factor of three increase in the number density of source galaxies available for lensing analysis. The dark core that is coincident with the X-ray gas peak, but not with any stellar luminosity peak is now detected with more than 10 sigma significance. The ~1.5 Mpc filamentary structure elongated in the NE-SW direction is also clearly visible. Taken at face value, the comparison among the centroids of dark matter, intracluster medium, and galaxy luminosity is at odds with what has been observed in other merging clusters with a similar geometric configuration. To date, the most remarkable counter-example might be the Bullet Cluster, which shows a distinct bow-shock feature as in A520, but no significant weak-lensing mass concentration around the X-ray gas. With the most up-to-date data, we consider several possible explanations that might lead to the detection of this peculiar feature in A520. However, we conclude that none of these scenarios can be singled out yet as the definite explanation for this puzzle.