Hi @Wittrin, Christian ,
Are you using Exchange Online or on-premises versions of Exchange server like Exchange 2019?
And how do the users access the Shared mailbox in OWA? Do they open the shared mailbox by clicking the profile in the upper right corner and then click Open another mailbox?
If the above is true, I tried testing in my Exchange online lab tenant using OWA, the templates created by one delegate can be stored in the My templates of the shared mailbox and then be used by another delegate who also has full access permission to the shared mailbox.
For the issue you described, do you mean the templates suddenly disappeared from all delegates' side?
Based on the discussion in this thread, you can try removing and then granting the access permission again to see the result.
Is there a way, like in the old Outlook, to save the templates as .oft files and import them back into the shared mailbox? Even sharepoint can only offer the file as a download. Wouldn't it make sense for these files to open from within sharepoint to owa? The locations only use the owa version.
As far as I know, I am afraid this is currently not feasible in OWA regardless of whether you are using Exchange Online or Exchange on-premises. Given this, I'd recommend sending the feedback to https://feedbackportal.microsoft.com/ . That way it becomes an official request to product Engineering and others can vote on the feature as well.
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