Some of the users have privilege to see “MyInbox” portlet in my application.
What i want to do is:
All users who can see MyInbox page will see the same “Saved Search” record on the “Save” tab of “Search Bar” when they open MyInbox page. The users won’t see another record in “Saved Search” drop down of “Save” tab and could not save any another “search filter”.

Does anyone know how to ensure that?

I’d like to clarify your question. I think you are asking:

1. Allow users to select from pre-defined searches
2. Don’t allow users to save their own searches.

Is that correct?