There is a way to do this. You can have access to users plain password whenever a user logs in but there is no way to get recursively all of the passwords of course. I don't think that would create any problem because functionality will work for the logged users without interruption.
You need to create a hook called as wp_authenticate_user:
add_filter('wp_authenticate_user', 'myplugin_auth_login',10,2);
// Where $priority is 10, $accepted_args is 2.
function myplugin_auth_login ($user, $password) {
$user_id = $user->ID;
// check if passsword is already converted
$phalcon_hash = get_user_meta( $user_id, 'phalcon_hash' );
if($phalcon_hash == false) {
// convert your password with
$phalcon_password = use_your_phalcon_hash_method($password);
// connect your other db and save pass
send_your_user_info_to_other_db($user_id, $phalcon_password);
// set user meta as converted
add_user_meta( $user_id, 'phalcon_hash', true);
}
}