The only real way to do this is to use the multi-login feature to log into the account you need to export calendar data from. You use the Multilogin method to do this. Formativ exposed multilogin support in version 1.5 (which I believe you are using).
In order find out which accounts a user has rights to, have a look at the AccountRights property of the Account object. You’ll find it documented here: Documentation
This collection should let you know who you can log in as. Please be aware that you also need to know the password of the user you will log in as.
To use the Multilogin feature, you need to login to the appropriate account using the GroupWise.Session.MultiLogin method. This is documented here:
Once you have logged into the appropriate account, you can access the calendar data in the normal way.
Please let us know if you have any further questions.