but is there any way for us to do this from the Exchange server when doing the move mailbox function? Also is there a way for us to get the rules back for this one user that lost them after the move?
Server-side Rules are stored in your mailbox, so ideally they should be carried over. So, you should check which rules are deleted - server-side or client-side ?
Secondly, to restore a rule - go ahead restore the database from previous backup to RSG, export the RULES using exmerge. Re-import using ExMerge or Outlook.