Need to replace IP address with FQDN in WP database

Due to circumstances beyond my control, I had to build a WP web site in the public folder of a hosting account that could only be accessed by it’s IP address rather than a fully qualified domain name (FQDN). The intended FQDN has now been pointed to the IP address and successfully resolves to the home page however all subsequent pages, posts, images, documents etc. continue to link through the IP address as one would expect.

If possible I would like to do a global search and replace through the WP database (MySQL) and substite the FQDN for the IP address rather than try to edit all of the posts, pages, links, etc. in the WP backend.

Is there a step by step process to accomplish this? (I rarely tinker direct to the WP database.) I trust some changes would also be necessary in the htaccess files and wp-config file. Or maybe some kind of redirect in the htaccess file(s) could make the FQDN appear rather than the IP address to the outside world.

The site is at http://www.staugpres.org.

Please advise.

Thank you.

Eric