How can deleted text messages recovered?

Did you delete them after installing iOS 16? Delete and recover messages on your iPhone or iPad - Apple Support

If you aren't running iOS 16, or you deleted the text messages prior to installing iOS 16 if they are in your backup you will need to restore your iPhone from that backup. You will lose any data added since the time/date of that backup.

Which iPhone are you using and which iOS version is installed on it?

If you deleted your messages while using iOS 16 on your iPhone, then you can check the Recently Deleted Filter in the Messages app and check to see if the messages are there to recover from. If not then read below:

Recover Deleted Texts

If iCloud is set to ON for text messages and you deleted some text messages then they are gone from iCloud so cannot retrieved!  If this is the case then it is all over and no need to read further. You can double check by opening Settings ➡️ Apple ID (Your Name at Top) ➡️ iCloud ➡️ Messages: If this switch is set to ON, then you are using iCloud for Messages.

 If you do not use iCloud for text messages then you can restore your iPhone from a backup on your iCloud account (if you use iCloud to back up your iPhone). Once you restore then your texts will only be as current as when the back up was created. Here is 👉 How to restore your iPhone from an iCloud back up.

The other option is to restore your iPhone from a backup that you may have created on your computer. Once again, if you restore your iPhone from a computer back up then your texts will only be as current as the day and time the backup was created. 

If you have a backup created on your computer and If you choose to restore your iPhone from your iPhone from it then here is how to do it 👉 Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Axel F.