No, nothing goes where the blue-ish orb-like object is between the Nature and Magic Factions on the Tech page. If you completed Puzzle 15, you should see the pearl as a key in the door in the Collections page. If you finished all 16 puzzles, then it sounds like you're finished except for the two awards you're missing. Then, you can keep your tribe going and check in on them or pause the game and go back to it. Maybe start a 2nd tribe?