Full paid version on iPhone, but restricted version on Mac

I’ve bought the full version (1 month) on my iPhone. Everything works fine there. When I open Budget Flow on my Mac, I can see my two budget books an can choose between them, but the app on the Mac is in the restricted mode and wants me to buy the full version. When clicking the button “Restore purchases” , the app says there are no purchases (German: “Keine Käufe vorhanden”). I use different Apple-IDs for the Store and for iCloud. But both Apple-IDs are within one Family Sharing-Group and sharing is active. Thank you & best regards, Tom