Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.
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Assuming the latter, are those users a member of any privileged groups (i.e. Domain Admins, Enterprise Admins, Schema Admins)?
If so, within the advanced security settings of the users, enable "Allow inheritable permissions..."
After enabling, the mobile users should have access to their mailboxes.
Reference...
https://technet.microsoft.com/en-us/library/aa998240(v=exchg.80).aspx