© 2016 American Physical Society. We study the lepton forward-backward asymmetry AFB and the longitudinal K∗ polarization FL, as well as an observable P2 derived from them, in the rare decays B→K∗+, where + is either e+e- or μ+μ-, using the full sample of 471 million BB-events collected at the (4S) resonance with the BABAR, detector at the PEP-II e+e- collider. We separately fit and report results for the K∗0(892)+ and K∗+(892)+ final states, as well as their combination K∗+, in five disjoint dilepton mass-squared bins. An angular analysis of B+→K∗++ decays is presented here for the first time.