If I understand your query correctly, then you are trying to deactivate the Adobe Export pdf on old computer to continue using it on new one?
Export pdf is a part of document cloud services and an online service that can be accessed from any computer and it also doesn't have the activation restrictions. You can access it from as many devices you want to.
Follow the steps mentioned below, to activate the subscription.
1- Export PDF is an online service that you can use online via: https://cloud.acrobat.com/exportpdf
2- You can also use the services through free desktop version of Adobe Acrobat Reader DC: Adobe Acrobat Reader DC Install for all versions
3- “Sign In” using the email (Adobe ID) under which you have subscription registered.
4- For detailed description of how to use the Export PDF service, you may refer to- Using Adobe Export PDF
You may refer to the following link for any troubleshooting: Troubleshooting Create PDF, Export PDF, Adobe Send, Fill & Sign … services(PDFPack or Document Cloud...
Let us know if it still doesn't work.