Thanks for using Apple Support Communities.
After reviewing your post, it sounds like iMessage doesn't work on this one device but works on others. You haven't mention if you can receive iMessages on the iPhone. This article addresses the issue you seem to be having.
iOS: Troubleshooting Messages
To resolve issues with sending and receiving iMessages, follow these steps
- Check iMessage system status for current service issues.
- Go to Settings > Messages > Send & Receive and make sure that you registered iMessage with your phone number or Apple ID and that you selected iMessage for use. If the phone number or Apple ID isn't available for use, troubleshoot iMessage registration.
- Open Safari and navigate to www.apple.com to verify data connectivity. If a data connection isn't available, troubleshoot cellular data or a Wi-Fi connection.
- iMessage over cellular data might not be available while you're on a call. Only 3G and faster GSM networks support simultaneous data and voice calls. Learn which network your phone supports. If your network doesn't support simultaneous data and voice calls, go to Settings > Wi-Fi and turn Wi-Fi on to use iMessage while you're on a call.
- Restart your device.
- Tap Settings > General > Reset > Reset Network Settings on your iPhone.
If you still can't send or receive an iMessage, follow these steps
- Make sure that the contact trying to message you isn't blocked in Settings > Messages > Blocked.
- Make sure that the contact you're trying to send a message to is registered with iMessage.
- If the issue occurs with a specific contact or contacts, back up or forward important messages and delete your current messaging threads with the contact. Create a new message to the contact and try again.
- If the issue occurs with a specific contact or contacts, delete and recreate the contact in the Contacts app. Create a new message to the newly created contact and try again.
- Back up and restore your device as new.
If you aren't receiving iMessages across all iOS devices
- Go to Settings > Messages > Send & Receive on each iOS device and make sure that you signed in with your Apple ID. You must use the same Apple ID on each device.
- Go to Settings > Messages > Send & Receive > You Can Be Reached By iMessage At and make sure that you selected each phone number and email address you want to use with iMessage.
- If you linked a phone number to your Apple ID with iMessage and the phone number hasn't appeared, followthese steps.
- Sign out of your Apple ID in Settings > Messages > Send & Receive and Settings > FaceTime on all devices.
- If you're linking a phone number to an Apple ID, sign in to iMessage on your iPhone first. Then sign in to the rest of your device one by one with iMessage and FaceTime.
Have a nice day,