send_core_update_notification_email

By default, administrators are notified when the update offer received from WordPress.org sets a particular flag. This allows some discretion in if and when to notify. This filter is only evaluated once per release. If the same email address was already notified of the same new version, WordPress won't repeatedly email the administrator. This filter is also used on about.php to check if a plugin has disabled these notifications.

// rejestracja funkcji zwrotnej — podaj liczbę argumentów!
add_filter( 'send_core_update_notification_email', 'twoja_funkcja', 10, 2 );

function twoja_funkcja($param_1, $param_2) {
	// Twój kod
}