How to Copy/Duplicate new user to another database

Dear All,

I was looking for a solution for that but couldnt find any.
I would like to copy/duplicate user info (while registering) to another database. In other words, while user is registering to blog A (database A), his user data (wp_user, wp_usermeta rows) is inserted into database A and database B (blog B).
I have to blogs but want users to register at Blog A while want to access Blog B. All other functions like updating stays the same – user update his meta in Blog A (registering blog).

Database A – user table is the same as Database B – User table

I guess it should be something like that:

(user.php)

$user = new WP_User( $user_id );

/ connetct with database B /

$user = new WP_User( $user_id );

/ close connection /

Can you help me with that please?

Thanks,

Primalism