Hi Juan - I agree with Gergely that SQLite is a better option than H2, as the database is more robust, performs great, have advanced features (ex: JSON support), evolves constantly, is fully extensible… In order to use SQLite on MOE, you have to compile the code and provide a JNI or JNA interface to the C functions.
We have done this work as part of our commercial platform “Darwino”. We have SQLite working on iOS with MOE, Android and even laptop/desktop OS with the regular JRE (MacOS, Windows…). Finally, we also integrated SQLCipher to get the DB encrypted.
As I said, this is part of a commercial platform but, if you’re interested by the database piece, please drop me a note at email@example.com