Auto login to a different website

I have a c# web application.

OnClick button on my website i want to autologin to this second website:
https://app.boi.gov.il/wad/PayeeSearch.jsp?type=1
and to load the inner page of the second website in an iframe on my website.

I have all 3 input details: ID, FNAME, LNAME

How do i do that?

Thanks