Cloned disk - duplicate disk signature, how to resolve?

You should be able to fix colliding disk signatures with the diskpart command line utility that comes with Windows. It allows you to view and change the disk signature.

Open a command prompt (cmd.exe) as administrator. Type:
diskpart and hit ENTER after each command;
the prompt changes to DISKPART>
list disk to get a list all mounted physical disks.
Now, type select disk xy, e.g. select disk 1.
after the disk is selected, type:
uniqueid disk to show the signature of the disk.
To learn more, type help uniqueid disk
To change the signature, type: uniqueid disk ID=NEWSIGNATURE
(I suggest to increasing or decreasing the (hexadecimal) id by 1, [1-9A-F])
Finally, type exit, then reboot.

Warning: Do this on your own risk.

As @Interminable said in the comment to the other answer, the solution for me was to just right-click on the offline disk and select 'Online'.