Processing account on website via client's info automatically

I have a website where clients will sign up. However, I want to use their information and to register an account on another website with their permission. The other site will also ask for some private questions to verify who they are, these questions need to be relayed to the client to be answered. The order of how this will work is the following: 1. The client will sign up on my website. 2. Either iframe the sign up page and fill in their info automatically, but I would prefer to sign up their info in the background and they will see a loading page. 3. The website ask the questions and we relay it to the client and we send it back to the website to verify their identity. 4. Once the account is sent through, I'll need certain information from that site to be displayed on our site.