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Sign in with your Apple ID – Apple Support
https://support.apple.com/en-us/HT204053

Your Apple ID is the account that you use to access all Apple services and make all of your devices work together seamlessly. After you log in, you can use the App Store, iCloud, iMessage, Apple Music, Apple TV+, and more.
Messages for iPhone, iPad, Apple Watch, and Mac – Official Apple …
https://support.apple.com/messages
Learn more about sending and receiving text messages, photos, personal effects and more with the Messages app on your iPhone, iPad, Apple Watch, and Mac.
If you can’t sign in to your iMessage account or FaceTime on your Mac
https://support.apple.com/en-gb/HT204408
If you can’t sign in to your iMessage account or FaceTime, one of these solutions may help.
If you can’t turn on or sign in to iMessage or FaceTime – Apple Support
https://support.apple.com/en-us/HT201422
To use iMessage or FaceTime, you need to activate them on your iPhone, iPad, or iPod touch. If you see an error message during activation, follow these steps.
Manage and use your Apple ID – Apple Support
https://support.apple.com/en-us/HT203993
Your Apple ID is the account you use to access Apple services like the App Store, Apple Music, iCloud, iMessage, FaceTime, and more. You can sign in to all Apple services with a single Apple ID and password.
Set up Messages on iPhone – Apple Support
https://support.apple.com/guide/iphone/set-up-messages-iph3d039b67/ios
Exchange text messages with SMS and MMS devices using your cellular connection on iPhone, and with other iOS devices and Mac computers using iMessage.
Access your messages on all your Apple devices – Apple Support
https://support.apple.com/guide/messages/access-messages-apple-devices-icht5b5d1e63/mac
In Messages on your Mac, use Messages in iCloud to access all your messages on all your Apple devices.
If you can’t turn on or sign in to iMessage or FaceTime – Apple …
https://support.apple.com/en-gb/HT201422
To use iMessage or FaceTime, you’ll need to activate them on your iPhone, iPad or iPod touch. If you receive an error message during the activation process, follow these steps.
Check your Apple ID device list to see where you’re signed in …
https://support.apple.com/en-us/HT205064
Learn which devices appear in your Apple ID device list, how to see your device’s details, and how to remove a device, if necessary.
Set up Messages on Mac – Apple Support
https://support.apple.com/guide/messages/set-up-messages-on-mac-ichte16154fb/mac
Set up Messages on your Mac with your Apple ID. Set up your iOS or iPadOS device with the same Apple ID and your messages are synced between devices.