Motivation: Alzheimer's Disease hallmarks include amyloid-beta deposits and brain atrophy, detectable via PET and MRI scans, respectively. PET is expensive, invasive and exposes patients to ionizing radiation. MRI is cheaper, non-invasive, and free from ionizing radiation but limited to measuring brain atrophy. Goal: To develop an 3D image translation model that synthesizes amyloid-beta PET images from T1-weighted MRI, exploiting the known relationship between amyloid-beta and brain atrophy. Approach: The model was trained on 616 PET/MRI pairs and validated with 264 pairs. Results: The model synthesized amyloid-beta PET images from T1-weighted MRI with high-degree of similarity showing high SSIM and PSNR metrics (SSIM>0.95&PSNR=28). Impact: Our model proves the feasibility of synthesizing amyloid-beta PET images from structural MRI ones, significantly enhancing accessibility for large-cohort studies and early dementia detection, while also reducing cost, invasiveness, and radiation exposure.