Generative approaches for cross-modality transformation have recently gained significant attention in neuroimaging. While most previous work has focused on case-control data, the application of generative models to disorder-specific datasets and their ability to preserve diagnostic patterns remain relatively unexplored. Hence, in this study, we investigated the use of a generative adversarial network (GAN) in the context of Alzheimer's disease (AD) to generate functional network connectivity (FNC) and T1-weighted structural magnetic resonance imaging data from each other. We employed a cycle-GAN to synthesize data in an unpaired data transition and enhanced the transition by integrating weak supervision in cases where paired data were available. Our findings revealed that our model could offer remarkable capability, achieving a structural similarity index measure (SSIM) of $0.89 \pm 0.003$ for T1s and a correlation of $0.71 \pm 0.004$ for FNCs. Moreover, our qualitative analysis revealed similar patterns between generated and actual data when comparing AD to cognitively normal (CN) individuals. In particular, we observed significantly increased functional connectivity in cerebellar-sensory motor and cerebellar-visual networks and reduced connectivity in cerebellar-subcortical, auditory-sensory motor, sensory motor-visual, and cerebellar-cognitive control networks. Additionally, the T1 images generated by our model showed a similar pattern of atrophy in the hippocampal and other temporal regions of Alzheimer's patients.