Record it and then simply make detailed notes or a transcript from the voice recording. The recording may not be useable (debatable), but your detailed diary notes of who said what should be.Um, that's about the business making the recording, not you. The laws about recording apply to the party who is taking action to make the recording. What the other party is doing is not related.
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They have a right to know that the other party is initiating a recording too. Implied consent would only be if you announce that you're making the recording and they continue with the call.