When you use ADMT to migrate groups, the Active Directory Migration log file may contain:
SID History cannot be updated for <group> because the SID for <group> already exists in the forest. rc=8539.
When you type net helpmsg 8539, it displays:
The source object's SID already exists in destination forest.
If you renamed the group and migrated it again, the SID would be duplicated. The SID must be unique in the forest.