It’s not a wordpress problem, it’s a DNS problem, so the best thing you can do is to ask your or their provider. Generally, I would ask their provider to point the DNS to your server.
In your end, to develop the site, I suggest to use a virtual host in your machine (for example using MAMP), so you can test with the final host. Otherwise you will need a find/replace on the DB when you activate the production site (and also adjust wp-config.php)
Hope it helps