The interfacing of quantum platforms via photonic links is a precursor for establishing scalable quantum networks. The connection of different types of quantum memories for hybrid networking requires the overcoming of the disparate photon wavelengths emitted by each quantum memory. Given achievements in quantum information processing with trapped-ion and neutral-atom architectures, a hybrid system with modular interconnectivity is advantageous. Here, we use a trapped Ba-138(+) ion and a periodically poled lithium-niobate (PPLN) waveguide, with a fiber-coupled output, to demonstrate 19% end-to-end efficient quantum frequency conversion (QFC) of single photons from 493 to 780 nm and use fluorescence of the ion to produce light at the Rb-87 D-2 transition wavelength. To demonstrate the quantum nature of both the unconverted 493 nm photons and the converted photons near 780 nm, we observe strong quantum statics in their respective second-order intensity correlations. This work extends the range of intralaboratory networking between ions and networking between disparate quantum memories.