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Installing WordPress / Moving WordPress

Hi There,

I have a questiion about moving and installing wordpress.

Here's my current setup. I an building out a wordpress site locally on my machine using MAMP. I need to move this site to the clients server. The catch is that I'm going to be installing this onto a web server that doesn;t have a domain name pointing to it. The client's domain name currently points to a different server. I can currently access their new website (which is blank right now) by typing in the IP address of the server.

So how do I go about successfully moving this site to their server?

I understand I will need to change the address of my Blog in my local wordpress settings to the (IP address?) and then I will need to export my local database, upload all of the files to the new server (edit wp-config.php with new credentials), import the database and I think that's it? Is it ok if I use an IP Address for my Blog settings rather than a domain name?

What happens when they want to point their domain name to the new server? Do I have to change anything behind the scenes in wordpress?

Thank you in advance for all of your help.