[Uniopolis]

You can open two connections. Use one to read from the source server, the other two insert into the destination server. Use the ON DUPLICATE KEY IGNORE option to prevent errors when you try to overwrite existing rows, so it only inserts the missing rows.

$pdo1 = new PDO('mysql:host=server1;dbname=xxx', $username1, $password1);
$pdo2 = new PDO('mysql:host=servrer2; dbname=xxx', $username2, $password2);

$insert_stmt = $pdo2->prepare("INSERT INTO yourTable (col1, col2, col3, ...) VALUES (:col1, :col2, :col3, ...) ON DUPLICATE KEY IGNORE");
$select_results = $pdo1->query("SELECT * FROM yourTable");
while ($row = $select_results->fetch(PDO::FETCH_ASSOC)) {
    $insert_stmt->execute($row);
}