I think this is possible.
Create a group called 'Group 1' or whatever.
Then on the forum where you are allowing them to post, set the permissions as normal.
On the forum you want to moderate, tick the 'post approval' box.
You can't have them in more than one group, so they will have a different group name to others and know they are being watched. - but then I guess they would know that only their posts are moderated anyway.