Long-term memory enables LLM agents to reuse past experiences, yet retrieving relevant memories does not necessarily provide sufficient evidence for answering a query. Essential information may remain fragmented across memory records, obscured by abstraction, or disconnected from the relations required for reasoning. We identify this relevance-sufficiency gap and propose QEMem, a framework that reformulates memory utilization as the construction of query-specific evidence sets, shifting the focus from individual retrieval relevance to collective evidential support. QEMem integrates three complementary mechanisms: query-guided discovery retrieves evidence across multiple memory granularities; source-grounded reification organizes it into structured ViewCards with explicit evidential roles and source references; and sufficiency-guided refinement selectively recovers missing information. Operating on existing memory stores without modifying memory formation, QEMem achieves 91.43% LLM-judge accuracy on LoCoMo with Claude Opus 4.5, outperforming the strongest evaluated baseline, MemR$^3$, by 7.6 percentage points and NEMORI by 10.7 points under a shared memory store. Further analyses demonstrate improved evidence coverage and strong performance on questions requiring cross-session evidence integration.

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