You need to copy the Logic folder from your user/application support folder from your old system. That is where the samples live, and that's is why you don't see them on your new system.
So.. go to your old computer, open the users folder and then the one that is your user name, then app support, and then Logic. Copy that folder onto a drive, and then put it into your new systems user folder, same place.
it's likely that Logic already created a new user Logic folder, so if you have made any new channel strip settings or made any new exs samples, be careful when you copy the new/old logic folder that you don't write over any new data.
The process of checking and removing, bla bla bla is too complex for me to go over how to do it on the lug; I suggest you get a more knowledgable Mac person to give you a hand, so you don't accidentally break your system while trying to fix something.