The paper considers the problem of beamforming design for a multi-cell network of downlink users, who either harvest energy or decode information or do both by receiving signals from the multi-antenna base station (BS) within a time slot and over the same frequency band. Our previous contributions have showed that the time-fraction based energy and information transmission, under which first the energy is transferred within the initial fraction of time and then the information is transferred within the remaining fraction, is the most efficient design alternative both in terms of its practical implementation and network performance. However, at the time of writing, both energy and information beamforming has only been implemented for proper Gaussian signaling (PGS), which has limited the network’s throughput. Although the network throughput could be improved in some specific scenarios by using non-orthogonal multi-access (NOMA), this may compromise the user secrecy. In order to circumvent the above implementations, we conceive improper Gaussian signaling (IGS) for information beamforming, which enables the network to substantially improve its throughput in any scenario without jeopardizing the user secrecy despite its low-complexity signal processing at the user end. A simpler subclass of IGS is also considered, which also outperforms NOMA PGS and works under any arbitrary scenario.