Map uploads dir to remote server

uploads-remote-nginx-apache.md

Nginx

Put this within server { ... } block of your vhost

location ~ "^(.*)/wp-content/uploads/(.*)$" {
    if (!-e $request_filename) {
        return 302 http://yourlivesite.com$request_uri;
    }
}

Apache

Place it under wp-content/uploads/ directory

<IfModule mod_rewrite.c>
  RewriteEngine On

  RewriteBase /wp-content/uploads/
  RewriteCond %{REQUEST_FILENAME} !-f
  RewriteCond %{REQUEST_FILENAME} !-d
  RewriteRule ^(.*) http://yourlivesite.com/wp-content/uploads/$1 [P,L] # use R=302 if P does not work

</IfModule>

NOTE: If the files are not being fetched from remote server, replace P flag with R=302, resulting it into [R=302,L] in your .htaccess file

Source