Your friend needs to keep track of her hours with pen and paper. Let payroll know about any mistakes on her pay check immediately. Supervisors are responsible for making sure the punches are recorded correctly.
The law requires the Employer to keep accurate records (though not necessarily in any particular form. An employee has no obligation to check their own punches, but, if they do not have some method of checking for accuracy it will be very difficult to prove they were not paid at a later date. Since this employer seems to have issues complying with Wage and Hour laws, it is probably a good idea to check whether the employees are getting uninterrupted 30 minute lunch breaks that are also mandated by law.
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She must be paid for the hours she works, so long as she can prove she worked those hours. But if the boss wants her to check her punches and make sure they are accurate then she had better do it.
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