The high-efficiency injection of a low-energy positron beam into the confinement volume of a magnetic dipole has been demonstrated experimentally. This was accomplished by tailoring the three-dimensional guiding-center drift orbits of positrons via optimization of electrostatic potentials applied to electrodes at the edge of the trap, thereby producing localized and essentially lossless cross-field particle transport by means of the E×B drift. The experimental findings are reproduced and elucidated by numerical simulations, enabling a comprehensive understanding of the process. These results answer key questions and establish methods for use in upcoming experiments to create an electron-positron plasma in a levitated dipole device.