  We report on quantum frequency conversion of memory-compatible
narrow-bandwidth photons at 606 nm to the telecom C-band at 1552$\,$nm. The
200$\,$ns long photons, compatible with Praseodymium-based solid-state quantum
memories are frequency converted using a single-step difference frequency
generation process in a periodically poled Lithium Niobate waveguide. We
characterize the noise processes involved in the conversion and by applying
strong spectral filtering of the noise, we demonstrate high signal-to-noise
ratio conversion at the single photon level (SNR$\,>\,$100 for a mean input
photon number per pulse of 1). We finally observe that a memory compatible
heralded single photon with a bandwidth of 1.8$\,$MHz, obtained from a
spontaneous parametric down conversion pair source, still shows a strong
non-classical behavior after conversion. We first demonstrate that correlations
between heralding and converted heralded photons stay in the non-classical
regime. Moreover, we measured the heralded autocorrelation function of the
heralded photon using the converter device as a frequency-domain beam splitter,
yielding a value of $0.19\pm0.07$. The presented work represents a step towards
the connection of several quantum memory systems emitting narrow-band visible
photons to the telecommunication wavelengths.
