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How long should it take an Amex AU to post?
Anywhere from 1-3 billing cycles once added. In my personal experience whenever I added someone it took only til the next statement but it's YMMV as always.
In my experience with adding me to my wife's ED account, it was reported with the next statement which is faster than they typically report newly opened accounts. Unfortunately, they now report AU account open dates as the date the AU was added rather than the account opening date. Seems that maybe they began doing that when they stopped backdating new accounts for existing cardmembers.