Moved from the Creative Cloud to the InDesign forum. They will be able to help you here.
Where is the font file? If it is in the packed folder of the old file you will find it in a Folder named "Document fonts". If your new document has not such a folder or the font is not inside this folder InDesign can't use it for the other document.
Is your Suitcase Fusion version compatible with CC?
Problem solved. Thanks Ken Rice, tht obviously helped.
Peter, yes, we had checked that yesterday, thanks.
Willi, That was plan b according to Adobe support. I'm pretty sure that packaging the file while in 5.5, then opening in CC would have worked.
Plan A (from Adobe support) worked which was copying the necessary fonts from the system (or from packaging the file in 5.5), into The fonts foler located in "Applications-->Adobe InDesign CC-->Fonts".
Thanks all for your help!
This is maybe an issue of 64bit vs 32bit Operating Systems.