We demonstrate high-quality distribution of $1.3\mu \mathrm{m}$ polarization-entangled photons generated from a fiber-coupled periodically poled $\mathrm{K}\mathrm{Ti}\mathrm{O}\mathrm{P}{\mathrm{O}}_4$ waveguide over $200\mathrm{m}$ fiber-optic cables. Time-multiplexed measurements with a 19% efficient superconducting nanowire single-photon detector at the remote location show a detected flux of $5.8\text{\hspace{0.17em}pairs}∕\mathrm{s}$ at a pump power of $25\mu \mathrm{W}$ and an average two-photon quantum-interference visibility of 97.7% without subtraction of accidentals.