sharing resources between two connected forests

We have two networks, each contained within it's own forest, both running
Windows 2003 Server AD. The two networks are connected. We have a directory
on network A that users on network B need access to. We have created accounts
on network A for network B users. Currently we have been having them create a
shortcut to the shared resource and they authenticate using their network A
credentials.

Question: If network B users map a drive to the shared resource on network
A, check off "Reconnect at Logon", and "Connect using a.." option ( with
their network A crednetials) should the drive get mapped the next time the
machine is restarted? They are complaining that the drive failed to get
re-mapped.

Thanks,
Kelly