For more information about features available in Skype for Business Basic in comparison to the Skype for Business client, please visit this page: Skype for Business client comparision chart Note: This Skype for Business Basic MSI desktop client provides presence, instant messaging and conferencing features. If you are licensed for Office 365.

Install Skype For Business

Hi Flemming,
Please try to restart Skype for Business when you cannot see the shared desktop. And also make sure Lync is not installed together with Skype for Business on your Mac.
Based on my test, the user can see the desktop sharing when he click the Skype for Business meeting url in Outlook or just double click the event in Skype for Business client.

Yahoo Messenger Desktop Client

So, here are some information I need to collect for troubleshooting:
1. The detailed version number of your Skype for Business for Mac and OS.
2. Do you join a meeting with the users in the same corp domain?
3. Please involve the admin to let me know if your organization have Skype for Business servers or you are only using Skype for Business Online
4. Try to log in to your account in another Mac and see if you can see the desktop sharing
5. Please try to confirm the client version and the Skype for Business/Lync server version of that person who shared the desktop. If other people shared the desktop to you via conferencing, can you see it successfully?
6. Screenshots of the symptom.
Thanks,
Alison