how to restore text conversation?

If your messages were synced with iCloud, it will not be possible to recover them. When you delete something on your phone that is synced with iCloud, it disappears completely.

If your messages were not synced with iCloud but were located locally on your iPhone, then you can try to restore from an iCloud Backup from the time they were available on the phone.

You can read here how to restore from an iCloud Backup:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Ryancombs Said:

"In accidentally deleted a text message conversation. How do I restore the conversation.

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Recovering Deleted Messages:

What to Consider:

A. Restore from Today's Backup:

Restore your iPhone from a backup of it that contains these messages, and you could recover them.

B. Check Messages App:

If messages was enabled on your iPhone along with your Apple computer, then check and see if the Messages app is enabled on your Mac to see if it exists in it. You'd start up your Mac, not connecting to the Internet, and open the Massages app. Then proceed from there with retrieving it. Important: Be certain you do not connect to the Internet while booting up, as syncing would delete it. So, power off your router to avoid the connection.

C.  Check your Carrier’s Site:

Log in to your Carrier’s site, seeing if you can view a history there. Doing so, I can see a call log going back 90 days —but not a text messages log.