EdgyWedgie found a work-around:
“On android at least, I’m using the Talkatone app, I paid $4 for one month of my phone number to be permanent then cancelled my sub for talkatone. The number works with Blizzards SMS protect.”
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I don’t think you can.
That’s why it’s important to activate the Battle.net Authenticator while you still got that number.
Because once that phone number is gone, the Authenticator is the only way you log in.
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So basically you just need 1 month of a new phone number.
Use that number to activate the Authenticator.
Then login using the Authenticator from then on.