Imitation learning (IL) has succeeded in enabling robots to perform new tasks by learning from demonstrations. However, its success is often constrained by the need for direct skill mappings between a learner and a demonstrator under identical conditions, limiting its adaptability to diverse environments and generalization across robots with different physical embodiments. To address these challenges, we introduce the Intention-Aligned Imitation Learning (IAIL) framework, a behavior adaptation approach that extends the conventional scope of IL by enabling robots to reproduce motions demonstrated by heterogeneous peers, even in previously unseen situations. Inspired by human cultural learning, IAIL aligns and adapts robot motions on the basis of high-level intentions annotated in natural language rather than by directly copying motor movements. This alignment is achieved by constructing a shared intention space that connects robot-generated motions with linguistic annotations, enabling inference-time behavior adaptation across diverse embodiments and environmental contexts. The framework further supports scalable task allocation in heterogeneous robot teams by leveraging differences in capabilities and constraints. We validated IAIL through real-world experiments involving seven distinct robots performing multistep collaboration tasks across 30 scenarios. Our results demonstrate that IAIL enables robust intention-aligned behavior adaptation across variations in embodiment, motion modality, and task configuration. These capabilities enable flexible behavior transfer across heterogeneous robots and support resilient, autonomous multirobot systems for reliable real-world collaboration.