Seems simple enough.
Either install Acronis onto the laptop (free trial should work) or plug in the external drive boot from the Acronis rescue media CD and browse to the .tib file you created as a backup.
If it truly is a "clone" rather than a backup (you seem to use both terms) then the same principle should work. I usually use the Acronis Rescue Media CD for these types of things and keep it away from the Operating System.
You may want to create a system image of the repaired laptop before moving forward just in case of any unexpected problems with the recovery.