Hook, line and sinker
To swallow something hook, line and sinker is to take the bait as it were and completely believe an unlikely story. It is an American expression from the early 19th century and derives from fishing. A fishing rod typically would have a hook with bait on it, a line and a sinker or lead weight that keeps the lure steady. Normally a fish would swallow the bait and hook only, but if it were to swallow the hook, the line and the sinker, it would have swallowed everything.