First, you need to set the 5th parameter of the FormsAuthenticationTicket constructor 'isPersistent' to true.

Then I would add change the code to this:

var faCookie = new HttpCookie("CookieFA", FormsAuthentication.Encrypt(authTicket));
if (authTicket.IsPersistent)
{
    faCookie.Expires = authTicket.Expiration;
}
Response.Cookies.Add(faCookie);

And if you also want to honor what's configured in web.config, you can add this extra code (optional):

var faCookie= new HttpCookie(FormsAuthentication.FormsCookieName, FormsAuthentication.Encrypt(authTicket));
faCookie.Path = FormsAuthentication.FormsCookiePath;

if (FormsAuthentication.RequireSSL)
{
    faCookie.Secure = true;
}

if (FormsAuthentication.CookieDomain != null)
{
    faCookie.Domain = FormsAuthentication.CookieDomain;
}
...