I don't see a specific question being asked, but I assume you want to know how to be able to stop the answering machine and the fax machine from answering calls @ the same time.
The easiest solution would be to order another telephone line and use it for the fax machine.
The only other option would be to purchase a device that "listens" for the polling beep that fax machines make and, if it hears it, sends the call to the fax. If it doesn't hear it, the call is sent to the answering machine.
Here is an example:
http://www.usr.com/products/telephony/telephony-product.asp?sku=USR4000
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