I don't think there is a way to do that at the moment. The text viewer can search but it doesn't have any knowledge of the last Find/Search operation, so you have to re-type (or copy & paste) the search string as you say.
There's no reason that couldn't be changed, though. It might be worth sending a feature request so it's added to the list of ideas.
The Grep Dir button on my Diff/Merge Toolbar may also be of interest, although it's not perfect. It'll let you type a string and then see a list of the files containing the string, and the lines that contain it. But the list appears outside of Opus so you then have to manually select the files.