You can not save a String object in EEPROM. The String is a pointer to some dynamically allocated memory, and not the actual characters of the message.
You need to convert your String to a character array, and save that in EEPROM.
General advice is not to use the String object because of memory fragmentation issues. Do you really need to use String objects instead of null terminated character arrays. With EEPROM use, you are going to need the character arrays anyway, so if you can work directly with them it will help.