Brushite, CaHPO₄×2H₂O, is a crystalline hydrated acidic form of calcium phosphate which occurs in biomineralization, albeit rarely, and in pathological crystallizations in humans, such as in kidney stone calculi. Additionally, it is biocompatible in humans and its possible use as cement for bone replacement is being investigated.  In this work, we perform a theoretical investigation of the vibrational spectrum of brushite. Within the framework of density functional theory (DFT), we predict not only the vibrational frequencies, obtained using the frozen phonon approach, but also their corresponding intensities by utilizing the Born effective charges tensor. This provides an unambiguous prediction, from first principles, of the experimental Fourier transform infrared (IR) vibrational spectra. Based on this, we are able to assert that the two doublets experimentally observed in the brushite IR spectrum originate from two crystallographically distinct water molecules, resolving a long-standing debate in the literature as to the assignment of these peaks.