It is not clear whether only players who received the Eon Ticket from an event distribution can share it with other players, or if players who obtain it via StreetPass can too. This function is likely inspired by the ability to share the Eon Ticket by mixing records in Pokémon Ruby, Sapphire and Emerald. In the Generation III games, only players who obtained their Eon Ticket from an e-Card or promotional event could share it with other players by mixing records.
As announced in last month's CoroCoro, a serial code to obtain the Eon Ticket in Pokémon Omega Ruby and Alpha Sapphire. This is the only currently announced distribution of the Eon Ticket for Omega Ruby and Alpha Sapphire.