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Users remain in one department in Active Directory since the only function of active directory groups is to get the user imported into the papercut database.
Users that print for multiple departments need to have the papercut client installed on their system, as per the links below. Printing is not affected by the client unless they are given access to more than one account within papercut.
Once the client is installed on the PC, send the windows server team a ticket with the accounts/departments the user is authorized to print for and the modifications will be made within papercut detailed in this article. Once the changes are made the user will get a popup when they send a print job to select the account to charge the job too. When the user logs into a printer to copy they get a similar pop up where they can click a list button to select which account they would like to charge copying to.
Windows client install:
https://ppm.smu.ca/TDClient/KB/ArticleDet?ID=305
Mac client install:
https://ppm.smu.ca/TDClient/KB/ArticleDet?ID=342