Set up Adwords conversion script in php

I have a registration page on WP; when the data is collected it automatically logs the person in to the site. At that point I'd like to fire the Adwords conversion script in PHP.

This is what I have at the moment but it doesn't seem to be working (obvs changed

// register the user using the WP function do_action('user_register', $user_id);              // google script for signup echo "<script>          gtag('event', 'conversion', {'send_to': 'AW-id_number'});     </script>"; 

Is there an obvious reason why this isn't working?

Thanks for any help here.