Is it possible in magento to redirect existing site one page to another website?
Without using htaccess and php header function.
Using magento code standard
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Url rewrites are working in a default Magento environment for external redirects, too. You can redirect almost every path of your store that way, because the check for redirects is done before other Magento routers come into action.
Therefore the rewrite in the below screenshot will do the redirect for your example.