Try simply starting up from the copy in "Safe Boot" - that is, hold down Shift from power on to the desktop. You'll only have to do that once.... and let me know if it works.

So should I put my cloned hd as starting disk and then when I power on my mac I have to press the Shift button?

Yes, hold down Shift from power on to the desktop.

Also necessary on ver. 2.6.1?
 

Just a single question: is it necessary to execute the script with the new version of SuperDuper 2.6.1, or was it only relevant for ver. 2.5?

It's only needed for v2.5.