Conversational agents that serve as lifelong companions must maintain persistent memory across all interactions. However, simply expanding context windows with raw retrieval degrades reasoning quality, while training memory agents via standard reinforcement learning creates a severe credit assignment bottleneck in a multi-stage pipeline. To solve this, we introduce SALIMORY, a framework that trains a single language model to manage a cognitively-structured memory-spanning user facts, preferences, and working memory. By introducing a hierarchical stage-wise process reward and reward-decomposed contrastive refinement, SALIMORY provides isolated supervision for distinct memory operations (selective filtering, consolidation, and cue-driven recall) end-to-end. SALIMORY cuts memory-attributed failures by one-third, outperforms the state-of-the-art by over 10% in end-to-end accuracy, and more than doubles the Good Personalization rate.