By default, the Altiris Helpdesk will match incidents on email subject lines looking for a match on '#nnnn', where nnnn is some number. As you've seen this creates a problem  when dealing with tickets which pass between multiple helpdesks.

The way I usually avoid this to modify the string the helpdesk matches on when parsing emails. Instead of matching on '#nnnn' for example, you can match on subject lines containing 'Incident #nnnn' instead. Only the Altiris helpdesk seems to use the 'Incident'   text prefix, so this usually works fine.

To do this, you'll need to change the contents of formats.xml in C:\Program Files\Altiris\Helpdesk\AexHD\bin.
Look for the line,

<string id="fmtEmailWorkItemPattern">#(?'number'\d+)</string>

and replace with,

<string id="fmtEmailWorkItemPattern">ncident #(?'number'\d+)</string>

Here i've chosen to match on just 'ncident' so that both Incident and incident prefixes will match -handy when you want to update tickets by firing specifically crafted emails into the helpdesk.

Note that formats.xml will be replaced on a AlertManager/Helpdesk repair, or upgrade. I tend to keep files like this tucked away in a custom folder which holds a batch script to replace files like this after performing any process which might 'downgrade' my mods.
 
Hope this helps,
Ian./