Finally fount this.
I had to perform an GET-Request with the parameters &sap-user=****&sap-password=***
. It is important to set them in the right order, as you can see following the link above.
Thanks!
Edit: Due to SAP-CRM-WEB-UI sends redirect and Cookies all in same request and HttpWebRequest ignores these Cookies for redirect, you have to handle this nanually (like explained here).