I'm sorry, I don't think there is a transfer feature like that in H2.
Maybe 'linked tables' will help however. See:
http://www.h2database.com/html/grammar.html#createlinkedtable
http://www.h2database.com/html/functions.html#linkschema
The idea is to create linked tables to the other database, then copy
the tables using:
CREATE TABLE X AS SELECT * FROM Y
and finally drop the linked tables.
You still need to create the constraints and indexes however.
Regards,
Thomas