After moving users to a different organisational unit you may find that you are unable to e-mail them using a dynamic distribution group. If the group was created in powershell you wont be able to edit it in the managment console either. It shows a message saying:
This Dynamic Distribution Group was created with the Exchange Management Shell. You can use the Exchange Managment Shell to modify the filter.
And all of the controls are disabled.
To update the recipient container from the Exchange Management Shell run:
Set-DynamicDistributionGroup -Identity DistributionGroupName -RecipientContainer ‘containername/ouname’