It looks like your theme doesn't support automatic search bar replacement. It probably uses a different hard-coded method to display the fullscreen search bar.
In this case the only option is to replace the search bar manually directly within the search theme files: https://goo.gl/8NlmBq
While it is not part of the support process I cannot guarantee this suggestion will work correctly, but I've downloaded and looked at the theme files, you can try the following steps:
1. Make sure to have a back-up copy of your theme and everything
2. Open up the wp-content\themes\jupiter\views\header\global\full-screen-search.php file via FTP
3. Change it's contents to this: https://goo.gl/GLPXPr
Now, after saving and refreshing the page, the ajax search pro search bar should be displayed instead of the default theme search in the full screen box.
If you need any help with the replacement, feel free to post temporary FTP details and I will do it for you.Best,
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