The character you know as "Sawyer" is really named James Ford. When he was a small boy, James Ford's parents were conned by a man named Sawyer, resulting in James' dad shooting mom before killing himself.

James Ford eventually became a con man, and took the name Sawyer as a fake identity. James Ford, our Sawyer, wrote a letter to the real "Sawyer," which James carried with him through his life intending to deliver when he found the con man. Along the way James travelled to Australia and killed a man he thought was the original "Sawyer" only to find it was not the man he sought.

James Ford never found the original "Sawyer," but we know the man was an accomplished con artist. Put that together with what we know about wealthy but secretive Anthony Cooper, if that is his name. He conned John Locke out of a kidney and he conned two other men out of $700,000 on a "Retirement Con" and made it sound like something he'd done before. No mourners at Anthony Cooper's funeral? That's because the man spent his life on the run, changing identities as he went.

Coincidence? Not on LOST. Anthony Cooper is "Sawyer."