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If you mean you want to change the links on your pages, then that is where you should make the change -- edit the pages or edit the script that generates those pages.
If you want to 'map' requests for example123.com into the filespace of example.com, then you can do that with mod_rewrite if both domains resolve to the same filespace on the same server. But that would create a duplicate-content problem and cause the two domains to compete with each other in search results, with neither doing as well as it could/would do alone. So, you'd want to redirect to avoid that problem.
Do not attempt to feed search engines the same content on two domains or even on two or more subdomains of the same domain. This is "duplicate content," and search engines don't like it -- And you will not be happy with their reaction to this.
Instead, pick one domain or the other, and redirect the second domain to that domain. Do not link to the second domain from your own sites, and do not promote that second domain in any other way on-line (you can still use it for TV, radio, mail, newspaper, and magazine ads if you like, though).