Of course, this gentleman doesn't actually claim to be the William Shakespeare -- he's just a William Shakespeare. Sam gushes that he's seen The Sound of Music at least a dozen times, before Shakespeare stops him short by telling him that the real William Shakespeare is dead. Sam is horrified, and asks if he left a wife and children.
It turns out this Shakespeare isn't even a William Shakespeare. He's just using it as his "nom de plum" (sic), to keep something of Shakespeare's legend alive -- "principally, his royalties."
Sam asks to hear a portion of one of Shakespeare's masterpieces, and "Shakespeare" looks around for an actor. He grabs the Swedish Chef as he passes by, and hands him the famous soliloquy from Hamlet to recite. It goes about as well as one might expect.