all the 22 other movies who uses Detective Conan

Do you have proof they were all originally released using Case Closed?

The question does'nt arise, they were all released in Japan. The real name is originally 'Meitantei Conan' and the 23 franchise's movies have this name. Case Closed or Detective Conan is a translated name for the manga, anime and movies.

Just for information, when Detective Conan appeared in the US, Funimation (an American company) translated with Case Closed due to legal problems with the name Detective Conan which was the original title. The first volumes of the manga, a part of the translated anime and the first six movies went by this name in the US. But then, Funimation have licensed everything and Shogakukan Asia (the Japanese publishing company of Detective Conan) made its own English language localized version of the manga and media adpatations which used the original title and Japanese names. Shogakukan Asia released again in the English translation with the original title.

That's why there is the name Case Closed during the early years of Dectetive Conan. But if you ask me, it's better to use the original title for all the movies

the first six movies went by this name in the US

If this can be confirmed, the first six movies should use "Case Closed."

Here's a link to the official japanese website for the movie, translated to english by the original publishers themselves:

https://web.archive.org/web/20200629181907/http://www.tms-e.co.jp/english/search/introduction.php?pdt_no=143

Detective Conan: Countdown to Heaven is the official english title.