Hello. I think the reason that the avatar is not appearing in FaceRig has to do with the way you copied its files in the Objects folder. You must put the exported files in a a folder with the avatar's name, then place that folder inside the Objects folder.

For example: Steam\steamapps\common\FaceRig\Mod\VP\PC_CustomData\Objects\avatar_name (wherein you have the avatar's .json files, its .cfg and the folder titled avatar_name.2048, or whichever resolution you exported it with, where its textures are placed).