NGINX proxy_pass with html hard links

I'm trying to run a web app listening on a different port of the same server. I'm using NGINX in order to proxy requests. I will show you an example to clarify.

server {
  listen 80;
  server_name example.org;
...
  location /app {
    proxy_pass http://localhost:8080/public/foo;
  }
...
}
...
server {
  server_name sub.example.org;
...
  location / {
    proxy_pass http://localhost:8080;
  }
...
}

When I go to http://example.org/app I can see the redirect is correct because I see the same html I can found at http://sub.example.org/public/foo, but the app at http://sub.example.org/public/foo/index.html includes some hard linked scripts.

<script type="text/javascript" src="/static/library.js"></script>

The console logs says that http://example.org/static/library.js can't be found, but this is obvious!

How can I modify the configuration in order to have index.html searching for http://sub.example.org/static/library.js?

You need to configure your upstream application's root URL to sub.example.org. Then the application generates correct URLs to resources it loads.