Motivated by a simultaneous explanation of the apparent discrepancies in the light charged lepton anomalous magnetic dipole moments, and the anomalous internal pair creation in 8Be nuclear transitions, we explore a simple New Physics model, based on an extension of the Standard Model gauge group by a U(1) B−L . The model further includes heavy vector-like fermion fields, as well as an extra scalar responsible for the low-scale breaking of U(1) B−L , which gives rise to a light Z′ boson. The new fields and currents allow to explain the anomalous internal pair creation in 8Be while being consistent with various experimental constraints. Interestingly, we find that the contributions of the Z′ and the new U(1) B−L -breaking scalar can also successfully account for both (g −2) e,μ anomalies; the strong phenomenological constraints on the model’s parameter space ultimately render the combined explanation of (g − 2) e and the anomalous internal pair creation in 8Be particularly predictive. The underlying idea of this minimal “prototype model” can be readily incorporated into other protophobic U(1) extensions of the Standard Model.