2018-05-30 Added "Export" feature (under "three dots" button on main screen's toolbar).Pocket MAL 4.8.16 Update
MAL is under maintenance for a long time and some users are afraid they will lose their lists. If you are stills logged in in the app you can extract your lists to .xml files.
What is going on with the app? (please read it carefully) - https://myanimelist.net/forum/?topicid=1731860