User memory helps personalized systems build on their understanding of users over time. In e-commerce, users convey their preferences and needs through both explicit language and implicit interactions with products. We study memory built from logs of these interactions, examining how it can \emph{remember} concrete evidence and established interests, and use that evidence to \emph{infer} underlying needs and preferences that inform judgments beyond well-observed product domains. Existing memory methods primarily target language-based interactions, and evaluations offer limited real behavioral data and limited separation of these capabilities. This leaves open how to jointly support and separately evaluate remembering and inference from behavioral logs. We formulate the problem of continual behavioral user memory around these joint requirements and develop a dedicated evaluation framework and memory method to address them. \textbf{BehaviorMemBench} is a benchmark built from real e-commerce logs covering 1{,}194 users and 17{,}462 behavioral batches over more than three years, with automatic future-behavior labels and a task-independent memory interface to separately evaluate remembering and inference under a common protocol. \textbf{BehaviorMem} is a memory design that organizes explicit behavioral facts and inferred user characteristics across long-term and short-term scopes in a two-axis state, with evidence-grounded formation, continual maintenance, and query-independent readout. Experiments across two builders and two task readers show that BehaviorMem leads the evaluated agentic memories on remember and infer, and reveal different method rankings across the two capabilities and competitive statistical baselines. Validation on a public dataset further supports its usefulness for downstream tasks based on behavioral histories.

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