If I am not mistaken, once you put a new hdd in a PS4, then the old one becomes obsolete for the PS4 data, so he will not be able to backup from the original.
Wait...What?
Nope, you are incorrect!
There are several ways to back up your games on the PS4 and his option are as follows:-
1) Reinstall the drive that was removed and use the "Backup Restore" option from the Settings of the PS4.
2) Insert the drive in an external enclosure, connect it to any PC and retrieve the system files for game saves.
3)Slave the drive using a "SATA and IDE Hard Drive Adapter to USB 2.0/3.0 works with 2.5" 3.5" and 5.25" Hard Drives and Optical Drives....and retrieve the data for the game saves.
Copy the data to the new drive.
Easy!