AltoBanor the only they this would be possible is if you booted from the external drive and then used the Help>Deactivate options within the application.
I would recommend that you migrate over only your documents and settings from the previous drive. Once this is done you can then reinstall on the new hard drive/computer. Once the installation is complete please activate the software. If you end up receiving an error at that time then please contact our support team to resolve your activation difficulties. You can reach chat support at http://adobe.ly/yxj0t6.
I believe this will be more expedient than trying to boot from your external drive. Also please make sure not to copy your applications from the external drive but instead install them. This is why I was specific with the suggestion to only migrate over your documents and settings.
