Is it obligatory to return the salutation of the deceased, and is the obligation to return it waived upon his death, and is salutation a right of the servants, or a right of Allah, or a right of both?

The default ruling for returning the greeting of Salaam is obligation, based on the Almighty's saying: "And when you are greeted with a greeting, greet in return with one better than it, or [at least] return it [in a similar manner]." This includes greetings sent via correspondence. There is no objection to returning the greeting of Salaam to the deceased, for it is a supplication for peace and mercy that the dead are in need of. It is a right of Allah and a right of His servants, for Allah Almighty has commanded it, and it has been authentically narrated from the Prophet, peace be upon him, that he said: "The rights of a Muslim upon another Muslim are five: returning the Salaam, visiting the sick, following funeral processions, accepting invitations, and saying 'Yarhamukallah' to one who sneezes."