Large-scale quantum networks will employ telecommunication-wavelength photons to exchange quantum information between remote measurement, storage, and processing nodes via fibre-optic channels. Quantum memories compatible with telecommunication-wavelength photons are a key element towards building such a quantum network. Here, we demonstrate the storage and retrieval of heralded 1532 nm-wavelength photons using a solid-state waveguide quantum memory. The heralded photons are derived from a photon-pair source that is based on parametric down-conversion, and our quantum memory is based on a 6 GHz-bandwidth atomic frequency comb prepared using an inhomogeneously broadened absorption line of a cryogenically-cooled erbium-doped lithium niobate waveguide. Using persistent spectral hole burning under varying magnetic fields, we determine that the memory is enabled by population transfer into niobium and lithium nuclear spin levels. Despite limited storage time and efficiency, our demonstration represents an important step towards quantum networks that operate in the telecommunication band and the development of on-chip quantum technology using industry-standard crystals.Many efforts towards future quantum networks [1] have focused on employing photons at wavelengths in the C band (1530-1565 nm) due to the possibility of lowloss transmission using existing fiber-optic telecommunication infrastructure. Local nodes in a quantum network are envisioned to process information using (optical) chips that are comprised of (elementary) quantum computers [1], while the synchronization of information is enabled by quantum memories that store and retrieve quantum information [2]. The latter underpins the operation of quantum repeaters, which promise to transmit quantum information through lossy channels or over intercontinental distances [3].Efforts to realize long-distance quantum communication have been bolstered by the significant progress of researchers to develop of quantum-optical technology [4]. However, much of this work is not compatible with Cband photons without the use of optical frequency conversion [5]. To avoid the conversion step, efforts have focused towards quantum technology that operates in the C-band, which has resulted in the development of efficient photon detectors [6] and single-photon sources [7]. Nonetheless, a C-band quantum memory has turned out to be particularly challenging component to realize and in particular so if it is to be integrated into a solid-state platform such that it is easy to integrate with other photonics components.Significant progress towards quantum memories has been made in the last decade, with most focus on the development of optical, microwave or radio-frequency to matter interfaces [8]. One promising approach to implement quantum memory is based on cryogenicallycooled rare-earth-ion-doped crystals as they often feature long optical and spin coherence times, as well as suitable energy-level structures [9]. Achievements with rare-earth-ion-doped crystals include broadband storage...