by Andreas Panagiotopoulos.
What do you mean to combine the two databases?
Are you going to have one database and one moodle site after the migration?
If not and you simply want to migrate the post-graduate moodle instance under a subdomain of the graduate program site, you should advice moodle migration here http://docs.moodle.org/23/en/Moodle_migration and make the appropriate settings to your web server (apache??).