Hi @afzal,
If you still need the help on this issue please follow the below steps:
Issue Symptom
The environment is Exchange 2016, one domain and one forest.
When try to add a user to a distribution group with Send As permissions through ECP and Powershell, would get the error: Couldn’t resolve the user or group. If the user or group is a foreign forest principal, you must have either a two-way trust or an outgoing trust.
Try with multiple distribution groups and multiple user accounts but all scenarios would get this error.
But there is no issue when adding a user with Send As permission to a mailbox.
Suggestions
Try to add the permission from Active Directory Users and Computers, test if the permission could be added successfully: Start Active Directory Users and Computers>>check Advanced Features from View>>find the related group from OU and right-click>>choose properties>>security tab>>add the user and choose the send as permission>>OK
If you add the permission successfully, but get error when send message with this permission, please check if the Send As permission has been assgined successfully:
Get-ADPermission -Identity <GroupName> | where {$_.ExtendedRights -like 'Send*'} | Format-Table -Auto User,Deny,ExtendedRights
If the permission is assigned successfully, you can try to restart the Exchange Information Store service from services page, then test again.
Thanks