When JeffersANT signs declaration, remember his signature - the same symbol you can see in the wall of the rotating room (behind the egg with JeffersANT). Leave the room and click the round symbol (on the blue wall close to the exit).
The puzzle with toothed faces and cannon
There is another puzzle - you need to join toothed faces and cannon. The lines between faces and cannon need to have a shape of JeffersANT's signature. On the left side should be two darker lines, on the bottom lighter (just as in JeffersANT's hint). There are many solutions to this puzzle. One of them - click: cannon, middle face, top-right face, cannon, bottom-right face, bottom-left face, middle face, cannon. Push the blue button. The right sequence is on the screenshot below.
Before you go through the door, click the dog. As Beaky jump on the green button (on the floor). As Tommy go left, pass three rooms (in the first one jump above the orange creature). In the fourth room push another orange creature to the left. The creature will hit the red button. You can do this only if Beak-Beak is standing on the green button. Go back to the dog, click Beaky and together go again left.
Now you can push smaller orange creature to the next room. Jump above the creature and go to the another room. As Beak-Beak stand on the blue button. Go back, jump above the creature and push it to the left. Go right and with Beaky go to the blue corridor with green button. As Beaky stand on this button.
As Tommy go left, push the orange creature next to the bigger one. Climb on the creatures and go left.
There is something flying here - a kind of bird. When it fells, pick it up and go back to Beak-Beak.