The reversible transfer of quantum states of light into and out of matter constitutes an important building block for future applications of quantum communication: it will allow the synchronization of quantum information, and the construction of quantum repeaters and quantum networks. Much effort has been devoted to the development of such quantum memories, the key property of which is the preservation of entanglement during storage. Here we report the reversible transfer of photon-photon entanglement into entanglement between a photon and a collective atomic excitation in a solid-state device. Towards this end, we employ a thulium-doped lithium niobate waveguide in conjunction with a photon-echo quantum memory protocol, and increase the spectral acceptance from the current maximum of 100 megahertz to 5 gigahertz. We assess the entanglement-preserving nature of our storage device through Bell inequality violations and by comparing the amount of entanglement contained in the detected photon pairs before and after the reversible transfer. These measurements show, within statistical error, a perfect mapping process. Our broadband quantum memory complements the family of robust, integrated lithium niobate devices. It simplifies frequency-matching of light with matter interfaces in advanced applications of quantum communication, bringing fully quantum-enabled networks a step closer.