Generally informing the other party you are recording is enough consent if they stay on the line. Plenty of customer service lines do that with an automated voi

Generally informing the other party you are recording is enough consent if they stay on the line. Plenty of customer service lines do that with an automated voice: "This call may be recorded (for quality control purposes)". So their party has already been informed that the call will be recorded, and there's no expectation of privacy.