1.Go ahead and select the desired old messages from the list, and click "Recover" to save them on your computer.
2.you can click on the "Messages" category on the left-hand side, and see a preview of specific text conversation on the right.
3.To retrieve old text messages from iPhone memory, connect your device to computer with a help of Lightning cable and launch the program. You will get a main screen shown below.
4.Proceed to Choose backup screen, then choose the backup you want to restore from in iCloud.
5.Sign into your iCloud account with Apple ID and password. The program won't save any of your information.
6.Repeat the same steps to turn off Messages in iCloud on your iPhone. When a notification pops up, select Disable and Download Messages.
7.The program will start searching for backup(s) you created in iCloud server and finally list them on the window, like the image below.
8.When ask you to sign in to iCloud, type in with your Apple ID and password.
9.When it's done, click the "Messages" category located on the left menu. You can preview any backed up message conversation by click the specific name before the phone number.
10.Launch iTunes and connect your device to the computer. If you're running a Mac with Catalina 10.15 version or above, open Finder app.
11.Wait for the sync to run. Uploading your old texts to iCloud takes a few time to complete, so you have to stay signed-in to your iCloud account the whole time.
12.Confirm the action by logging with your Apple ID. A few minutes later, you will be greeted with a HELLO screen prompting you to set it up as a new device.
13.Click "Start Scan" to take a deep scan on the device. Be patient, as the whole process might take a while. Once the scan is end, you will get an overview window, indicating how many of data files it found.
14.When you see the device icon appear in the top left corner, click it. In Finder, select your device name under Location on the left side menu.
15.Click Standard backup. Or select Encrypted backup if you want to keep the data secure.
16.Once logged in, uncheck other types of items, click the blue iCloud Backup, followed by Start.