It is best to spell this out in the policy. The moderator needs to determine how cross-posted articles are going to be handled for the group. In other cases the moderator's policy may state that cross-posting will never be done, or will be done only at the moderator's discretion. This is a little unfair to the submitter if the moderator does not inform the submitter of the situation. There is nothing wrong with this policy but the moderator should assure that the group's readership is aware of the policy.
Articles are sometimes cross-posted to multiple moderated groups.
In those cases, it is important to make sure that moderators of all groups have approved the article before it is actually posted.