Problem in register activation hook and Copying folder

You are defining the recurs_copy() function to perform the copy but you never execute it. Try:

function hyperbolic_activate() {

   $src="https://wordpress.stackexchange.com/questions/112547/includes/myTheme/";
   $dst="../themes/";
   recurs_copy($src, $dst);

}
register_activation_hook( __FILE__, 'hyperbolic_activate' );

function recurs_copy($src,$dst) {
    $dir = opendir($src);
    @mkdir($dst);
    while(false !== ( $file = readdir($dir)) ) {
      if (( $file != '.' ) && ( $file != '..' )) {
         if ( is_dir($src . "https://wordpress.stackexchange.com/" . $file) ) {
            recurse_copy($src . "https://wordpress.stackexchange.com/" . $file,$dst . "https://wordpress.stackexchange.com/" . $file);
         } else {
            copy($src . "https://wordpress.stackexchange.com/" . $file,$dst . "https://wordpress.stackexchange.com/" . $file);
         }
      }
    }
   closedir($dir);
 }