Hello ercatihw,
Thanks for the post in Apple Support Communities. That's a great question about the green phone icon you're seeing on your Apple Watch, and we have a resource that may explain what's happening.
Does it look like the icon shown below, from the resource titled If your Apple Watch isn't connected or paired with your iPhone?
If you don't get notifications, messages, or calls on your Apple Watch, your Apple Watch and iPhone might not be connected. When your devices disconnect, the red iPhone icon or the red X icon appears on your watch face. You can also check your connection in Control Center. When your Apple Watch connects again, the green iPhone icon appears.
First, bring your Apple Watch and paired iPhone close together. If you still see that the devices are disconnected and need help, try the steps below. After each step, see if your devices can connect.
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Based on the above, it sounds like there may have been a connection issue between the Apple Watch and iPhone. Has this happened more than one? Were you able to use the functions of your Apple Watch after this happened?
If the issue has happened again, it might be a good start to restart both devices and see if that helps:
Restart your iPhone
How to restart your Apple Watch
Kind regards.