Your cleanest solution is to create matching user accounts in the new domain either by hand, script or migration via ADMT. Then on the old email server, export all mailboxes using ExMerge. You can then import the PST files created by ExMerge into the new server.
For the Public folders it is easiest to copy them to a PST from a workstation on the old domain then use an Outlook client on the new domain to import the data back in.
I hope you find this post helpful.
Regards,
Mark