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In lifelong learning, we wish to maintain and update a model (e.g., a neural network classifier) in the presence of new classification tasks that arrive sequentially. In this paper, we propose a learn-prune-share (LPS) algorithm which addresses the challenges of catastrophic forgetting, parsimony, and knowledge reuse simultaneously. LPS splits the network into task-specific partitions via an ADMM-based pruning strategy. This leads to no forgetting, while maintaining parsimony. Moreover, LPS integrates a novel selective knowledge sharing scheme into this ADMM optimization framework. This enables adaptive knowledge sharing in an end-to-end fashion. Comprehensive experimental results on two lifelong learning benchmark datasets and a challenging real-world radio frequency fingerprinting dataset are provided to demonstrate the effectiveness of our approach. Our experiments show that LPS consistently outperforms multiple state-of-the-art competitors.