In simple words my theory is- Momonosuke retained Oden's memories just like he inherited the ability to hear Zou and order it.
The voice of things is an ability that only D clan people were able use/show so far in the story- Only they were to hear Sea kings and other things.
So My guess is Kozuki clan might also be a part of this infamous D clan. They are the ones who made the actual Poneglypps.
And to safeguard this knowledge n information to read n write the Ancient Poneglypps Kozuki clan had- they developed some way of passing it through the memories of Main family line i.e Oden and now Momonosuke. Or simply said this ability is probably just specific to their clan( just like Three eyed eyed can read Poneglypps). Like from father to son , from one generation to next memories passed through Centuries.
It explains how he had Rodger n Inu-Neko being Friends memories (even tho hazy) from 24 years ago even tho he is just a kid. So yes i do believe those Graves are fake.
Also equal Credits to @Buusatan94.