User Interface:

1. Open Exchange Management Console.
   
2. Expand Microsoft Exchange On-Premises, then right click Recipient Configuration, click Find... in popup menu.
   
3. Input group name, then click Find Now.
   
4. Double click the result. Then click Group Information tab. We can see the Managed By part. Click Add... to add owner of this group.
   

   

PowerShell:

1. Open Exchange Management Shell.
   
2. Check current owner of the distribution group.
   
3. Add new owner. Remember to add original owners with the result above.
   

   If we don’t use parameter BypassSecurityGroupManagerCheck, we will see below error.
   

4. Check distribution group owner again.