On construction sites, the assembly of building components is a predominant task. Although its automation is still in its infancy. This paper presents a concept and implementation of a capability matching and a multi-agent approach for precise and heavy material handling on construction sites. The crane primarily carries the weight and moves components over long distances, while the robot performs fine positioning. The implementation includes a communication strategy between the crane operator and an automated industrial robot with a newly developed end effector for moving heavy components by decoupling vertical loads. The research highlights both potential and challenges of crane-robot collaboration. While heavy components can be handled under controlled conditions, wind impacts can cause unpredictable swaying of the crane boom, affecting the robotic system. Despite these challenges, the implementation shows great potential for automated assembly in the construction industry.