I think it has something to do with string matching. Often this menu disappears after translating an application from english to some other language. I filled some bug reports to nokia about that help menu in their development tools and the answer was something like: It is not documented by apple how to do this. Sometimes it works, sometimes not.
I believe simply creating a menu named 'Help' in the main menu bar on a Mac will cause this search field to appear. I have not been able to discover how to provide results for the search however.
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