If both databases reside on the SAME MySQL server (and use the same user and password to connect). You simply establish the connection without picking a database, then put the name of the database in front of the table name like:
INSERT INTO myDBname.myTableName (myKey) VALUES (myValue);
If you have a connection to one database you can change it before inserting:
$pdoConnetion->select_db('myDBName');
INSERT INTO myTableName (myKey) VALUES (myValue);