Does that team still exist in some name shape of form? Yes
Did he finish one of those TDFs that do that have an official winner? Yes
Any after that? Yes, but not after the period of Tours with no winner.
Does his last team in fact still have at least part of the name they had when he rode for it?
Is it currently a WorldTeam?
He didn't finish a Tour after 2005?
Does his last team in fact still have at least part of the name they had when he rode for it? Yes
Is it currently a WorldTeam? No
He didn't finish a Tour after 2005? He did not