Hello Reinhardsechs,
As per the description above, you are not able to find the serial number for Adobe ExportPDF service, Is that correct?
The record shows that you are subscribed to Adobe ExportPDF service on your current Adobe ID, you can access the service through the URL https://cloud.acrobat.com/exportpdf with your Adobe ID and password on a browser like Chrome, or Firefox, or Safari.
Note: Adobe ExportPDF is an online service which cannot be downloaded as an application on a computer and it does not require any serial number for activation. However, we can access the services through a browser and can be accessed through desktop and mobile app Adobe Reader DC.
You can download and install the freeware Adobe Reader DC which does not require any serial number for activation and you can access the service of Adobe ExportPDF, just "sign-in" with your current Adobe ID and password in Adobe Reader DC.
To download Adobe Reader DC use the URL Adobe - Adobe Acrobat Reader DC Distribution
For troubleshooting, you can refer to Troubleshooting Create PDF, Export PDF, Adobe Send, Fill & Sign … services(PDFPack or Document Cloud Services).
Feel free to update this discussion for any further assistance.
Regards,
Anand Sri.