You can move your decorations between aquariums using the Store:
1. Tap a decoration to open the menu below it.
2. Tap the box icon in the menu, and the decoration will disappear from the aquarium, appearing in theStoretab.
3. Go to a different aquarium and open the Store.
4. Stored decorations are marked Stored. Tap the decoration, and in the next window tap Place.
5. Enjoy your decoration in its new surroundings!