Hi GioSp,
Re: "iMessage troubleshoot: My father and I: we could text everyone else with iMessage , except between us"
You might want to check whether an iOS update is waiting to be installed : You can check in Settings > General > Software updates, iOS 26.0.1 is the latest update.and it contained bug-fixes, security updates, and more.
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Reminder: If you choose to update, it is always wise to back-up the iPhone before updating the iOS version.
Else: If already using iOS 26.0.1, you might want to try restarting the iPhone instead. (ie: Deletes temporary files, re-establishes connections, may update recent setting changes, and often restores order if something is not working as expected.
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Re: :"Whenever i text him the arrow pointing up is green and inside the text frame it says "Text messages * RCS".
Can you please help me out whats wrong ?"
You might want to see: What is the difference between iMessage, RCS, and SMS/MMS? - Apple Support
Wondering whether the wi-fi signal was not strong enough at the time to send those messages between you and your father. If the messages went by cellular data instead, and your plan isn't set up for that, the messages may not have been delivered. The update mentioned above may improve that wi-fi situation.
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iMessages go between Apple devices by by wi-fi: (Blue bubbles)
To turn iMessage on or off, go to Settings > Apps > Messages.
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To use RCS, you need a text-messaging plan from a carrier that supports RCS
To turn RCS on or off, go to Settings > Apps > Messages > RCS Messaging.
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SMS / MMS are carrier-provided services
To use SMS/MMS on an iPhone, you need a text-messaging plan that supports these services.
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If your wi-fi signal is not strong enough at times for iMessages default settings send as cellular data
Eg: wi-fi Assist switches messages from wi-fi to cellular data (Green bubbles)
If needed: You can turn off Wi-Fi Assist.
Go to Settings > Cellular or Settings > Mobile Data. Then scroll down and tap the slider for Wi-Fi Assist.
If needed: View or change cellular data settings on iPhone - Apple Support
Eg: says:
Set cellular data usage for apps and services
Go to Settings > Cellular,
then turn Cellular Data on or off for any app (such as Maps)
or service (such as Wi-Fi Assist) that can use cellular data.
If a setting is off, iPhone uses only Wi-Fi for that service.
Hope something here will help restore order :-)