Hi Faisal,
Thank you very much for the proper details. I logged in via sFTP and looked up the header search location. It is hard-coded in the includes/header-search.php file, which made it not automatically replacable.
I made this same file in the child theme directory, and replaced the search source code with the plugin shortcode, you will find it in the salient-child/includes/header-search.php file. Now it will display the plugin search bar instead of the built in one.
I would also recommend adding this custom CSS code to have the plugin better positioned:
[html].wpdreams_asp_sc-1 {
width: 90% !important;
margin-top: 48px !important;
}[/html]
Please note that this qualifies as a customization request, so I cannot guarantee that my solution will work properly in all cases. Nevertheless, I still hope I did help you out, the best way I could.