In the twenty-third Case Closed film, The Fist of Blue Sapphire, the legendary blue sapphire dubbed the "blue lapis fist" supposedly went down with a pirate ship near Singapore in the late 1800s. A wealthy local entrepreneur intends to recover this gem, and once it goes on display at the Marina Sands hotel in Singapore, a murder occurs, accompanied by a bloody calling card from Kaitou Kid.
Concurrently, Ran and Sonoko travel to Singapore for a karate competition. Conan, unable to leave Japan because he lacks a passport, is supposed to stay behind. However, Kaitou Kid, in need of Conan's aid, uses a magic trick to forcibly bring Conan to Singapore. To return home, Conan must cooperate with Kid, but first he has to disguise himself since his glasses, watch, and other belongings are taken away.
When Ran fails to identify him, he calls himself "Arthur Hirai." Later, Kid discovers that the "fist" is stored in a concealed vault beneath a mansion. As he thinks he has safely accessed it, a dangerous trap is set off. He then confronts Makoto Kyogoku, the undefeated karate champion boasting 400 consecutive victories.