Rules for Pearl Transfer:
Purchased pearls and gems are carried over to your Eternal Island at the end of a round.
Earned pearls (earned in Quests) are not carried over and expire at the end of the round. However, they are always spent first when you make a purchase with pearls.
Purchased pearls and gems are automatically carried over when you start a new world.
If you finish two rounds before starting a new one, everything from both rounds is carried over into the new world.
There is no manual transfer between game worlds.