Red-teaming work has shown that adversarial suffixes found by the gradient-based Greedy Coordinate Gradient (GCG) algorithm can jailbreak aligned LLMs, but GCG is computationally inefficient, which limits study of how such suffixes transfer across models and data. This paper connects search efficiency to suffix transferability through DeGCG, a two-stage transfer learning framework that decouples the search into behavior-agnostic pre-searching and behavior-relevant post-searching, along with an interleaved variant i-DeGCG. Experiments on HarmBench show gains across models and domains, and the analysis highlights the role of first target token optimization in transferability.