After you send keys, set a global variable say
bool login_initiated=true;
Handle the link click invocation in the document completed event..
you need to add a event handler on some event like form load etc.
webBrowser1.DocumentCompleted += new WebBrowserDocumentCompletedEventHandler(webBrowser1_DocumentCompleted);
protected void webBrowser1_DocumentCompleted(object sender, WebBrowserDocumentCompletedEventArgs e)
{
if (login_initiated == true)
{
webBrowser3.Document.Links[15].InvokeMember("click");
}
}