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Multi-Robot and Multi-Agent Systems demonstrate collective (swarm) intelligence through systematic and distributed integration of local behaviors in a group. Agents sharing knowledge about the mission and environment can enhance performance at individual and mission levels. However, this is difficult to achieve, partly due to the lack of a generic framework for transferring part of the known knowledge (behaviors) between agents. This paper presents a new knowledge representation framework and a transfer strategy called KT-BT: Knowledge Transfer through Behavior Trees. The KT-BT framework follows a query-response-update mechanism through an online Behavior Tree framework, where agents broadcast queries for unknown conditions and respond with appropriate knowledge using a condition-action-control sub-flow. We embed a novel grammar structure called stringBT that encodes knowledge, enabling behavior sharing. We theoretically investigate the properties of the KT-BT framework in achieving homogeneity of high knowledge across the entire group compared to a heterogeneous system without the capability of sharing their knowledge. We extensively verify our framework in a simulated multi-robot search and rescue problem. The results show successful knowledge transfers and improved group performance in various scenarios. We further study the effects of opportunities and communication range on group performance, knowledge spread, and functional heterogeneity in a group of agents, presenting interesting insights.