Patient-specific finite element (FE) models of the breast have received increasing attention due to the potential capability of fusing images from different modalities. During the Magnetic Resonance Imaging (MRI) to X-ray mammography registration procedure, the FE model is compressed mimicking the mammographic acquisition. Subsequently, suspicious lesions in the MRI volume can be projected into the 2D mammographic space. However, most registration algorithms do not provide the reverse information, avoiding to obtain the 3D geometrical information from the lesions localized in the mammograms. In this work we introduce a fast method to localize the 3D position of the lesion within the MRI, using both cranio-caudal (CC) and medio-lateral oblique (MLO) mammographic projections, indexing the tetrahedral elements of the biomechanical model by means of an uniform grid. For each marked lesion in the Full-Field Digital Mammogram (FFDM), the X-ray path from source to the marker is calculated. Barycentric coordinates are computed in the tetrahedrons traversed by the ray. The list of elements and coordinates allows to localize two curves within the MRI and the closest point between both curves is taken as the 3D position of the lesion. The registration errors obtained in the mammographic space are 9.89 ± 3.72 mm in CC- and 8.04 ± 4.68 mm in MLO-projection and the error in the 3D MRI space is equal to 10.29 ± 3.99 mm. Regarding the uniform grid, it is computed spending between 0.1 and 0.7 seconds. The average time spent to compute the 3D location of a lesion is about 8 ms.