Kann man mit dem Lightroom Downloader die Bilder anschliessend wieder im Lightroom importieren?

You can either use the Lightroom Downloader Tool to export everything to your hard drive and reimport everything into your new account OR alternatively use the shared album and contribute route, which hopefully should work, you could try this....
 
• Create Album on Personal account.
• Enable Sharing for that Album.
• Invite email ID associated to your Work account.
• Ensure you give the Work account Can Contribute rights.
• Accept invite associated with Work account and sign in to Work account
• Add Photos to the Album that’s shared with you from the personal account.
 
This will transfer photos over including edits without having to export the photos.

You could transfer all photos to that one Album and sort them from there. However it maybe easier to mirror your Albums in the new account and share each one (although you will have to accept an email for each album).