I’m no constitutional scholar, but can’t a president serve for ten years? I’m not sure anything precludes Obama from taking over as president for another that has left office with two years or less left in his/her term. I wouldn’t expect that, because it doesn’t make sense to start a new campaign with someone not already in the White House if you can help it.
"No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of President more than once."
So, since Obunghole was elected twice, he cannot serve again as President.
(Since Trump was elected ONCE, for one term, I take it to mean he CAN be elected to one more term.)