Or you can make a button which adds to AdminCC of a ticket all watchers from former queue when moving the ticket to another queue. Then your Department A creates a ticket in their queue and move it with mentioned button to the queue of Department B.
This button can be added for example before the ticket history. Add the code:
<FORM ACTION="<% $RT::WebPath %>/Ticket/ModifyAll.html" NAME="MoveTicketToQueueWithAdminCc">
<input type="submit" value="Move ticket to (with AdminCc)">
<& /Elements/SelectQueue, Name => 'Queue', %ARGS, ShowNullOption => 0, ShowAllQueues => 0 &>
<input type="hidden" name="WatcherTypeEmail" value="AdminCc">
<input type="hidden" name="WatcherAddressEmail" value="<%$Ticket->QueueObj->AdminCc->MemberEmailAddressesAsString%>">
<input type="hidden" name="id" value="<%$Ticket->Id%>">
/opt/rt4/local/html/Callbacks/SA/Ticket/Display.html/BeforeShowHistory and take a look at that. Would this help?