Download and run PhoneRescue on your computer. Log in to your Apple account and password, and then choose the backup you wish to recover. From there, select the messages you want to recover and click the right arrow button to continue. This software will scan the backup file and recover the messages. Once you have recovered your text messages, you can simply import them into your computer. You can also export the messages in various formats.

See also - https://emailspedia.com/recover-deleted-text-messages-on-iphone/