You need two connections, one to each database.
If you want the two operations to be a single unit of work, you should use XA JDBC drivers so you can do two-phase commit. You'll also need a JTA transaction manager.
This is easy to do with Spring.
SELECT from one connection; INSERT into the other. Just standard JDBC is what I'm thinking. You'll want to batch your INSERTs and checkpoint them if you have a lot of rows so you don't build up a huge rollback segment.
I'd wonder why you have to duplicate data this way. "Don't Repeat Yourself" would be a good argument against it. Why do you think you need it in two places like this?