One Registration Form for Two Websites – One Site Completely Anonymous

I’m not sure how to ask this question because I’m a novice with WP, but here goes. I have two websites with different url’s. Users will go through the full registration process on site A, complete with User Name and Password, and they will then be directed to site B where they will choose another User Name and Password. The entire point of this is to shield my users identity completely, meaning no connection to their original registration/identity on site A. All email communication will be on site A, so site B will be completely anonymous even though I registered the users on site A.

I’ve been stuck on this problem for a while now and I have no clue how to even approach it, let alone solve it. The normal registration process would be ok on site A, but the email requirement on site B defeats the entire purpose of what I’m trying to do. Any help or guidance would be appreciated.

Thanks in advance. These forums have helped me considerably as I’ve built my websites.