There are two Obama achievements that haven’t come to full fruition yet and, as a result of timing, might end up being things that the Republicans and Trump would take credit for.
The first is the economic recovery. Right now the country has been on a slow but steady economic upswing; however, if it continues on its upwards trajectory during the next few years then that could be something that ends up being credited to Trump and the GOP instead. Of course, Trump might try to meddle in it and end up harming the economy and sending it plummeting downwards again instead - when if he had done literally nothing maybe the economy would just keep on going up. So Democrats have a tough dilemma in rooting choices: Root for Trump to meddle in the economy and make it fail, thus making 2020 an easier election for the Democrats, or hope Trump just lets the Obama recovery continue, but take credit for it?
The second is that ISIS is now on the ropes and on the verge of collapse and defeat. Already it is losing Mosul and is being shattered on the inside and out. But after years of Republicans criticizing Obama for a purported “weak ISIS policy” (which in fact has actually been rather effective,) the final defeat of ISIS may take place during the Trump administration - which is merely the culmination of the anti-ISIS campaign put into steps by Obama years earlier. So again Trump and the GOP might take credit for it.
Any others?