Fine-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks. We formalize this failure as the \textit{\textbf{Knowing--Using Gap}}, characterized by an accuracy gap and a temporal lag between memorization and generalization. To understand this phenomenon, we fine-tune LLMs with unseen knowledge and monitor the spatial permeation dynamics of the knowledge internally using a novel intervention technique called self-patching. Self-patching identifies activation locations where relocating representations substantially improves failed generalization cases. These results are consistent with a knowledge-circuit misalignment hypothesis: memorized representations can exist internally but may not be routed to computation-effective layers. To demonstrate the practicality of this diagnostic finding, we design a simple heuristic strategy which recovers 58--75% of the oracle headroom in generalization failure. Experiments are done cross-domain for the robustness of this finding.