No. Robot movements are usually initiated by programs stored in motion control units or computers, rather than in end effectors.
These programs typically contain a series of motion instructions that control the robot's individual joints and limbs to achieve the desired motion trajectory and movement.
End effectors typically contain only work actuators that are relevant to a specific task, such as grippers, laser cutters or sensors.
Therefore, the robot's motion instructions are usually not stored in the end effector.