The error messages in Danish:
Indstillingerne for stedfortrædere blev ikke gemt korrekt. send på vegne af-liste kunne ikke aktiveres. Du har ikke den nødvendige tilladelse til at udføre denne handling på objektet.

The error messages in English:
The Delegates settings were not saved correctly.
Unable to activate send-on-behalf-of list.
You do not have sufficient permission to perform this operation on this object.

Solution:
In order to resolve this you need to give Write Personal Information permission to the SELF account on the user who is trying to add the delegate. To do this, follow these steps:-

Connect to your mail server.
Open Active Directory Users and Computers, and then click Advanced Features if it is not already selected on the View menu.
Expand your domain, and then locate the user’s Organisational Unit (OU).
In the right pane, right-click the user who is experiencing the delegate issue, and then click Properties.
Click the Security tab, locate the SELF account, and then click “Write Personal Information” and “Read Personal Information”.
Click OK