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I have exactly the same situation and have both domain names pointing to the same IP address.
That is your best solution.
There are two other solutions if you don't want to use that one for some reason.
The first is to place a Redirect or Rewrite directive in the .htaccess file in the root of one domain so that it will redirect all traffic to the other doamin.
The other solution is to put an index.html file in the root of one domain so that it will redirect all traffic to the other domain. This is the worst of the three solutions and I would recommend you not use it.