New Appointments not uploaded to iCloud Calendar

Since a week or two I’ve got following problem:

When I add a new Calendar item to my iCloud calendar in eMClient it perfectly appears in emClient. However, it is not synced to the iCloud and thus not to other iDevices.

Sync in the other direction still works. E.g. a new appointment from my iPhone is perfectly synced to emClient.

What can I do to fix this? I’m using emClient for Windows 7.2.34062.0.

Best
Nils

I found the “Repair” feature for calendars - which might help. However: How can I backup the non-synced appointments before using the “Repair” feature, in order to re-import them, after repairing the cal?

Hope you can help. My wife’s calendar is on icloud. My calendar is on Google. She is unable to “invite” me to join appointment on her calendar. 
Any ideas how to do that?