Are the memories still there? If someone from the royal family was to inherit the Founding Titan, then the predecessors' and future successors' memories would transfer to him/her as well.


But,


  Eren's father steals the Founding Titan and then passes it down to Eren.


So, are the memories gone? Or will they come back if a true member of the royal family 


  retrieves the Founding Titan back?
Spoilers from up to Chapter 107.



According to the wiki,


   only those with royal blood—the Fritz or Reiss royal families—are able
 to use the true power of the Founding Titan. However, if the Founding
 Titan is inherited by someone outside of the royal family, the power
 can still be used if the inheritor is in physical contact with a
 Titan with royal blood. This is demonstrated when Eren Yeager
 temporarily used the Founder's power after striking the hand of Dina
 Fritz's Pure Titan. It is implied by Zeke Yeager that it does not
 matter if the Titan of royal blood is a Pure Titan or one of the Nine
 Titans, such as the Beast Titan.


 If the inheritor touches a human of royal blood, although the full
 power of the Founding Titan is still locked, some snippets of the
 previous inheritors' memories can be realized. The touch of Historia
 Reiss and her father Rod occasionally resurfaced the memories of
 Grisha Yeager. However, these memories are erratic and do not always
 come.


So if


   a true member of the royal family regains the Founding Titan, I assume that they will be able to see all of the previous memories again. Naturally, they will be subject to the First King's Will.