It is possible to send someone else's snap, but it is against the terms of service for Snapchat. If you are caught sending someone else's snap, your account could be banned. When you send a snap, it goes through Snapchat's servers and is then sent to the recipient. Because of this, Snapchat can see that you have sent a snap that was not originally yours. While it may be tempting to send someone else's snap, it is not worth risking your account being banned.