I process payroll for a not-for-profit organization and I share an office with someone who does not report her time truthfully on her timesheet. She arrives late, takes 1 1/2 hour lunches, and often leaves before completing her 8 hour day. Our manager is not aware of this abuse so he continues to sign her inaccurate timesheets. Do I have an obligation as payroll processor to report this?

I would say yes. Falsifing time cards is theft, and is usually grounds for termination. I think that you should have a conversation with your manager about your concerns. Some companies have an anoyomus report line.

Yes, you have a moral obligation to tell your boss and your company, someone is stealing from the place you work. Little by little this effects everyone.

I work for a national payroll company and the situation you described is a big NO NO. The biggest question I would ask is: If you bring this up and terminate the employee, is that how it's outlined in your employee handbook. Also if you haven't begun to document the incidents I would do so immediately, and as detailed as possible.