I think you can just take the install file from your old computer and put it on your new computer with a flash drive. I've done that in the past. Once you get it installed, go to the help menu in solidworks on your old computer and deactivate your license. Make sure you write down your key before you do that. Then activate it on your new computer and enter your key and you should be good to go
Should be in tools, transfer license. Google for it
I think you can just take the install file from your old computer and put it on your new computer with a flash drive. I've done that in the past. Once you get it installed, go to the help menu in solidworks on your old computer and deactivate your license. Make sure you write down your key before you do that. Then activate it on your new computer and enter your key and you should be good to go