The Minhag of saving a piece of afikoman is not only in chutz laaretz, but anywhere, and it’s not in case you don’t have for next year.
The reason is that it’s a “shmira” (protection).
Many hang it on top of a doorway until the next erev pesach when they burn it with the chometz.
This minhag is brought down in basically every minhag sefer (minhag yisroel torah, nitei gavriel, and other pesach seforim).