Method 1: Recover Lost Photos Stream of the iPhone with the backup file
Instead of retrieving all the data from iTunes, you can restore selected data from iTunes backup file. In this case, you need to resort to iPhone Data Recovery Tool, which has the Windows and Mac versions.
You don 't have to connect your iPhone to PC. Just download and run this tool on your computer. Then switch to "Recover from iTunes backup files", select your iPhone's backup and click the "Start Scan " button to scan your iPhone. When the analysis is complete, browse photos one by one under the "Photo Stream", then select the items you want to recover.
Method 2: Recover lost iPhone Photo Stream without backup file
As long as you stop using your iPhone after you have deleted photos by mistake, you can also use iPhone Data Recovery Tool, a pure program to recover iPhone lost photo stream. Since the deleted photos may be replaced by the new data when you use your iPhone to take pictures or something. So, after your lost or deleted photo stream, perform recovery as soon as possible. To get a better understanding of this program, you can try the trial version before buying.
Step 1. Download, install and launch iPhone Data Recovery Tool on your computer and connect with iPhone via USB cable.
Step 2. Wait until the software automatically detects your iPhone and click "Start Scan" button.
Step 3. Under "Photo Stream" category you can preview all your lost photos. You can select the photos you want and recover them or transfer them to your iPhone.