This is an ASP.NET question ? You say you have a 'page', but you did not tag your question as ASP.NET. How do you create a file locally ? I can only assume you mean that the user downloads the file. As it's created on the server, it's the server that should then copy the file to the other server, if they are on a network, OR the other server should impliment a webservice which you can call to pass the file over.
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Is there an easier way of achieving this? Just a simple way of passing credentials and paste a file on the remote server
Web services are trivial to write, so I don't know there's an 'easier' way at all, but for there to be an alternative way, the machines need to be on the same network, and not just connected by the internet.