If you have a USB drive and you might be able to transfer it.
Connect the USB drive to the ps4, and then go to settings from the main menu.
You should see an option called "Application Saved Data Management". Select it.
Then you have 3 options: Saved Data in System, Saved Data in Online Storage, and Saved Data on USB. Select "Saved Data in System Storage".
From there, select "Copy to USB Storage".
Then you can choose Fallout 4 and select it for backup.
If you are wanting to transfer the save between accounts, then try relogging into your account from the ps4. If you are wanting to move your save file to a different ps4, then plug the USB into your ps4.
Go back to to the Data Management screen and this time select "Saved Data on USB Device". You should have an option that says "Copy to System Storage".
See what that does for the save file and let me know.