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The answering machine is presumably on the same line as the fax.
In which case, you may need to get 'Distinctive Ring' service from your phone service provider. This provides two numbers that both ring the same line, but with a different ring pattern. You may set the fax to recognize the ring style for its number, and not respond if the ring style is the other number's style for the voice phone, leaving it open for the answering machine to pick up on the line instead.
There may be other solutions to fit your preference, but this is the usual way to deal with such a situation, with regular landline service anyway.