HTTPS requests get converted to HTTP

In order to make this work, you'll need several thigns:

1. A virtual server configured for TCP port 443, configure an HTTP profile
2. A client SSL profile, which is to be assigned to the virtual server. The client SSL profile (when configured with an SSL certificate/key pair) will terminate the SSL session at the BIG-IP. The choice of certificate to use on the BIG-IP is yours, but it should be something that users aren't going to receive security warnings for. Ideally it would be issued by a publicly trusted CA.
3. A pool with the server or servers specifying their port as 1080 as scenario three depicts. Apply this pool to your virtual server.

That should be about it. If you want to dig deeper into any of the above steps, just ask. Not sure your level of familiarity with BIG-IP so I kept it simple.