I get the idea that the article (which I already read some years aog, probably because it was mentioned here) just describes the route to the article "Proof of the Umbral Moonshine Conjecture", for which a pre-print appeared on https://arxiv.org/abs/1503.01472

For many mathematical pre-prints can be found at arxiv.org or at the authors website. Searching for the article title with "PDF" usually returns them.