The map file provided by OsmAnd for a particular region has inaccuracies, so I would like to use this fixed OBF file instead.
How to do that?
Below is the procedure described on the website providing the fixed map, unfortunately it did not seem to work (when viewing the whole country the regions downloaded within OsmAnd (official OBF files) are highlighted in green, but the non-official region does not show in green).
First, uninstall any standard OsmAnd maps of the region, because they will conflict with your custom map.
Copy the map file to the Android device. If you have downloaded the map file from this site, be sure to unzip it first.
For example, use a network-capable file manager, such as ES File Explorer.
Put the map into the osmand data folder (you can check which it is under Settings → General → Misc → Data folder )
It seems that the map needs to be renamed once within OsmAnd's Map manager (Map management → Local → Select your file → Rename) before it is actually recognized by OsmAnd.
Afterwards, don't forget that you have to change the description language (Configure map → Description language) to English to see the transliterated place names.
Also, as the base world map has not been created using JapanMapTranslate, you will need to zoom in a bit so that your local map is actually used.
Note: Unlike my other question How to import a .obf POI file in OsmAnd this question is about maps, not POIs. Answers at that question do not solve the problem here.