Society is undergoing a relentless digital transformation process. This process is creating a digital copy of every entity present in the physical world and these digital goods will be inherited through centuries establishing a direct link between distant generations. Advances in artificial intelligence make the promise for future whole brain emulation enabling the possibility of uploading the human mind on a digital system. This would enable the possibility of interacting with immortal digital clones of deceased people. This paper wants to start investigating the consequences of the emergence of the concept of digital immortality.