AWU cannot send sms to Android users

Yes, it should. This indicates your cellular provider has not provisioned your account for your watch correctly. You need to work this out with your carrier.

This happened to me once, long ago and it turned out AT&T, my carrier didn't have either the IMEI or ICCID number coded correctly in their system. That may or may not be your issue, but clearly something is wrong on their end.

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SMS texting requires an iPhone connected to the internet (either through Cellular or WiFi), or an Apple Watch with cellular capability.

You mentioned you have an Apple Watch Ultra, which has cellular capability. In this case, your carrier has not provisioned your sim to send and receive SMS from your watch. I recommend you contact your carrier.

Check this Article for more information: Use your Apple Watch without your iPhone nearby - Apple Support

Hope to have helped,

Raymond

What you've posted is correct IF the poster is using a 3rd party app to send messages. If they are using the built in Messages app on their Apple Watch, which is Apple's app and most certainly NOT 3rd party, I don't believe the iPhone is required to be powered on if you have a correctly provisioned Cellular Apple Watch.

I could certainly be wrong. But what you posted specifically says 3rd party apps.

It may be. Accessing a network is different than cellular communications, which requires going through your carrier to speak between devices.