You can purchase a special visitor egg for a friend! If a special visitor arrives in your forest and you wish to purchase an egg for your friend as a gift you can do this! The egg will show up in their forest in a nicely wrapped package. Simply tap the icon that looks like a shopping basket and person then you can choose a friend from your friends list.
You can only send one special visitor to one friend once a day. If you decide to purchase for a friend you cannot then purchase that same egg again for yourself and will need to wait for this butterfly to visit you again!