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Now it shows up on Outlook, but they don't sync, aka if one girl delete's an email, when the other girl logs on it's still there on her machine so she thinks it hasn't been handled.

If they are using a shared mailbox, if one person deletes the email/reads the email it should be reflected in the other's mailbox. There 's a slight delay of 15 seconds before it is updated on the Exchange Server. Then once the Exchange Server is updated with the change. It will take 30 seconds before the client downloads this change. Using Categories/Color Codes is still much better for tracking and sorting purposes as Bert so nicely demonstrated in his video. These are the registry keys to change the update interval. (Not recommended)As Bert and I mentioned earlier, categories is the best way to do it.
Key: HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\<version>\Outlook\Cached Mode

Value name: Download
Value type: REG_DWORD
Default value: 0000001e (30 seconds)

Value name: Upload
Value type: REG_DWORD
Default value: 0000000f (15 seconds)

Value name: Maximum
Value type: REG_DWORD
Default value: 0000003c (60 seconds)