This is for version 1.40 and higher. For older versions, go here.
You can download maps for Omega Centauri's LunarMap HD for Android inside the app simply by selecting them in the "Choose map" menu option or here. If you download them here, please put them in your device's Android/data/mobi.omegacentauri.LunarMap.HD/files/maps (or .Lite for the Lite version) folder on its external storage.
If you're still having difficulties, email OmegaCentauri.
LROC data provided courtesy of NASA/GSFC/Arizona State University. The LRO WAC grayscale mosaics were further processed by John van Vliet and later Omega Centauri Software, licensed under Creative Commons cc-by-sa 3.0 license. Creative contributions to LRO WAC grayscale mosaics copyright (c) 2008-2011 John van Vliet (http://www.celestiamotherlode.net/catalog/moon.php).