This is not possible with EasyDiscuss because it isn't a registration system. In other words, all the registration links in EasyDiscuss are pointing back to Joomla's core registration.

If you want something more sophisticated, this is possible with EasySocial. When you invite someone to the site and they click on the link in the email, you will be assigned points and you will be a friend of that person once he registers on the site

I am trying to integrate the AlphaUserPoints it works but it override the easydiscuss point to alpha user point. Do you have any possible fix to this?

Unfortunately if you configured EasyDiscuss to use AUP, it'll then use AUP as it will not use points from EasyDiscuss.