I know on HP fax-capable printers (and may apply to your Brother also) they specify that the telephone line to the fax must be a 2-wire cord, not a 4-wire cord. They are both the same size plastic ends but on a 2-wire cord only 2 of the pins on each end have wires on them.
UPDATE:
While looking for an image to post with 2 vrs 4 wires, I saw this page on Brother. They also talk about the wire.
https://help.brother-usa.com/app/answers/detail/a_id/152634/~/problems-sending-faxes4. Verify that you're using the telephone cord that came in the box with the Brother machine. If you're using a different telephone cord, that could be causing the problem.
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The telephone cord that came with your machine has only two gold wires in the clear connecting end. If the telephone cord you're using has four wires, it's not the cord that came with your machine. You'll need the telephone cord that came in the box with your
2 wire cord
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On Obi 2-line devices, the LINE1 port has 4 wires and allows 2 phones to be connected via 1 wire. This is like a single cable to a 2-line phone. 2 of the wires is one line and the other two wires are line 2. The LINE2 connector only has 2 wires and is only line 2. Thus plugging in a device like a fax machine to the LINE1 port and not using just a 2 wire cable, the fax machine may route the ring back into the LINE2 port.
Connect the fax machine using only a 2-wire cable and you should be fine regardless of which LINE port it is in.