A sufficient advanced civilization could also send to others a way to build some sort of Artificial Intelligence mimics original one. For example for a robotic, AI or post-singularity civilizations this could be similar to mind uploading, but no from real world into some virtual reality but to another part of the galaxy.
With similar point in mind a communication between two species could be complete and game-changing for receiving civilization. Imagine impact on earth if first discovered message could be decrypt (I think it's possible to decrypt almost anything, but is my point of view, maybe using something related to physics, like structure of hydrogen or water) and become an IA able to self-thought and communication abilities.