On Wednesday, he had a rough start against Belgian contender Kimmer Coppejans, but then improved hig game on several levels to win 4-6, 6-1, 6-2.
This means he is through to the final round of the qualifying tournament for the year's second grand slam tournament. He now faces the Italian Matteo Gigante, who is ranked 167 in the world.
Elmer Moller had difficulties finding his rhythm in the first set against Kimmer Coppejans, and even though he was the first to secure a break of serve, he went on to lose the set.
Clearly upset, Moller used his frustration to playing with more energy and initiative while he also took bigger chances and hit far more winners.
The slightly more unpredictable style caught Kimmer Coppejans off guard time and time again, and Elmer Moller won the set convincingly.
He maintained his level in the third and decisive set, where Moller had great outbursts of joy after winning decisive points.
Elmer Moller in total produced 44 winning shots, which clearly exceeded the 17 he hit during his win against Facundo Bagnis in the first qualifying round.
August Holmgren was also in search of advancement to the final qualifying round on Wednesday, but was beaten by Thiago Agustin Tirante from Argentina.
Holger Rune has already secured a place in the French Open due to his high position in the world rankings.