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My wife is an authorized user on my American Express Blue Cash Preferred. (She uses it primarily for groceries, so we can get the 6% back.)
I don't recall setting anything special up -- I just ordered her a card when I first opened the account. But whenever one on her charges shows up on the account, it has a little icon next to it that indicates it's hers. And I can break out her charges and analyze them the same way I can mine or the whole account together.
She used it on online one time, and I did get the card-not-present email. So the notifications seem to come to me.
Account Services -> Card Management -> Additional Cards and Custom Limits
From there you can add spend tracking alerts, set spending limits or freeze the card.
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