I've searched inside of folgunthor and searched the dead adventuror and it is not there, any help? I do not know where to go next.
First off, make sure you searched the correct dead adventurer:
Head upstairs and locate the dead body of Daynas Valen leaning against another dragon claw trigger. Examine his body for the ivory dragon claw and his essential notes; make sure to read them as instructed.
If for whatever reason he truly doesn't have the claw and you don't remember getting rid of it anywhere, then the only option at that point is to add it via command console:
player.additem 0008cdfa 1
Of course, this only works on the PC version. There doesn't seem to be any alternatives for the console versions.