A refined derived Torelli theorem for Enriques surfaces

We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from 2 are isomorphic if their Kuznetsov components are equivalent. We apply the same techniques to give a new simple proof of a conjecture by Ingalls and Kuznetsov relating the derived categories of the blow-up of general Artin-Mumford quartic double solids and of the associated Enriques surfaces.