Using WP_List_Table and search_box(): How to Paginate the Found Search Results When Sending by Method «Post»?

This issue I have also faced and suggestion the solution

By adding this much javascript to update the pagination links using jquery by adding search in page links.

if($("#listing-tbl").length) {
        if($("#search-search-input").length) {
            var search_string = $("#search-search-input").val();
            if(search_string != "") {
                $("#listing-tbll .pagination-links a").each(function() {
                    this.href = this.href + "&s=" + search_string;
                });
            }
        }
    }