This is how Trump will reveal his ruse (being a Democrat in disguise). He will appoint Obama to his ticket, to run as his VP.
Whilst the 22nd Amendment (ratified in 1947) makes Obamas third term unconstitutional, there is a legal argument that Obama could run as VP. Then Trump could somehow fall over (or other misdemeanour) and Obama soldiers on.
Apparently this wouldn’t work in legalese, and indeed, Hilary was advised against recommending Bill as her VP because the 12th Amendment states that no person constitutionally ineligible to serve in the office of president, shall be eligible to that of VP. (But note it says “eligible” and not “serve”).