In this article, we propose a lightweight blockchain-inspired framework-Magnum-as a magazine of transfer learning models in blocks. We propose the storage of these blocks on proximal fog nodes to simplify access to pretrained base models by industrial plants to tune them before deployment. We design Magnum for B5G-enabled scenarios to reduce the block transfer time. We formulate a demand-centric distribution scheme to further reduce the search and access time by adopting a nonlinear program model and solving it using the branch-and-bound method. Through extensive experiments and comparison with state-of-the-art solutions, we show that Magnum retains the accuracy of the models and present its feasibility with a maximum CPU and memory usage of 80% and 6%, respectively. Additionally, while Magnum requires a maximum of 10 s for writing models as large as 17 Mb on the blocks, it requires 16 ms for fetching the same.