It is necessary to implement a link transition in order to get to the link of the affiliate program prepared by me in advance, how to do it?

Question

Web development

Good day to all! I ran into a very interesting problem and I can't figure out how to solve it.

I have a site. On which the button is located - when clicked, the user must go to filling out the form (this is another site) of the affiliate program. What's the point you ask. IN THE IDEA, it is necessary that the user follows the link of the affiliate program, clicks on the button there to fill out the form and receive all the codes and further actions, but I need it a little differently!
It is necessary to do this: the user, while on my site, clicks on the button and goes straight to filling out the form (as if he followed the direct link of the affiliate program and clicked on the button there to fill in all the data) and receive all the codes and further actions, for all this, it should count to me as an application under the affiliate program link. Please help .... I'm racking my brains and I can't implement it either. A friend said that smart guys on Habré will definitely help! I keep my fingers crossed for you and I believe that you will help