In large-area quantum networks based on optical fibers, photons are the fundamental carriers of information as so-called flying qubits. They may also serve as the interconnect between different components of a hybrid architecture, which might comprise atomic and solid-state platforms operating at visible or near-infrared wavelengths, as well as optical links in the telecom band. Quantum frequency conversion is the pathway to change the color of a single photon while preserving its quantum state. Currently, nonlinear crystals are utilized for this process. However, their performance is limited by their acceptance bandwidth, tunability, polarization sensitivity, and undesired background emission. A promising alternative is based on stimulated Raman scattering (SRS) in gases. Here, we demonstrate polarization-preserving frequency conversion in a hydrogen-filled antiresonant hollow-core fiber. This approach holds promises for seamless integration into optical fiber networks and interfaces to single emitters. Disparate from related experiments that employ a pulsed pump field, we here take advantage of two coherent continuous-wave pump fields.