No direct connection exists between Animal Crossing: Wild World (DS) and the Wii console. They cannot communicate, share items, or transfer towns.
Animal Crossing: City Folk (Wii, 2008) included a **one-time transfer tool** to import your Wild World town:
This required Nintendo WFC (shut down 2014). It no longer works.
Wild World on DS and City Folk on Wii are separate games. The one-time transfer tool is dead. Enjoy Wild World locally or via flashcart mods.