INSERT INTO Trees(ParentId, ForestId)
SELECT Id, @NewForestId FROM Trees
WHERE ForestId = @OldForestId;

UPDATE T2
SET ParentId = T3.Id
FROM Trees AS T1
JOIN Trees AS T2
ON T1.Id = T2.ParentId
AND T2.ForestId = @NewForestId
LEFT JOIN Trees AS T3
ON T1.ParentId = T3.ParentId
AND T3.ForestId = @NewForestId;