I think Moon is giving Trump one last chance to get a deal Trump and Kim can both live with. However, I more than suspect that Moon will make his own deal with Kim if Trump can't pull off a deal in a reasonable time. Moon knows that the two Korea's can't go on as they have and that they need to unify regardless of what any other nation or nations may or may not want. I believe Kim is smart enough to know all of that too.
South Korean President Moon Jae-in told U.S. President Donald Trump in a call on Tuesday that his country is willing to open economic engagement with North Korea as a "concession" if it will hasten Pyongyang's denuclearization, Moon's office said. [Source]