If you have cloned your Mac to an external HD, then with some applications you could simply copy it from the Applications folder on the cloned drive to the original.
But it depends on the application. Take a look in User/[your user name]/library/application support/
for any files that may belong to that application. Copy them to the same location on the Mac.
I would advise you to install the applications again in the case of Logic ad other large app's that have a lot of files across your system.