Hi @Elisabeth Sanson ,
I want to get text message alerts when receiving emails from certain people
Did you mean that the "display a specific message in the new item alert window" option in Outlook rules that works like below?
If so, I have tested on my Outlook 365 version 2104(Build 13929.20086), but the alert window could work normally there. So what's the version of your Outlook client(File>Office account>About Outlook)? And have you tried to test on other accounts in your Outlook?
Also, corrupted rules may also cause it, it's also suggested to re-create a rule for testing.
In order to further confirm your issue and perform more tests on my environment, please provide us with more information about your issue.
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