First, of course, you will want a copy of the letter, as it may contain references to the law, to her hours worked and the guidelines and regulations that you need to appeal against. So, the letter, in your hands and complete with any attachments.
It would also help if you have the name of a contact person at the employer’s HR office (or equivalent) to discuss questions that may arise as you compose the appeal. I would suggest a friendly information-gathering call (you may need to submit some form of power of attorney signed by your mother first, before they will agree to talk with you – I would suggest that you have that ready beforehand so that you can fax it or email a scanned copy immediately.) That kind of readiness will at least demonstrate that you’re not completely ignorant of the legal and security issues that the employer will have in discussing such matters with someone other than the principal – your mother. (I’m pretty sure that you can find power-of-attorney and healthcare-power-of-attorney forms online or in any decently stocked office supply store. So have that ready and available, or ask the company representative if they have a form of their own that they want you to fill out for your mother’s signature, which will allow the conversation to begin. Obviously, it would help to have your mother present during the discussion to avoid long communication lags between questions that they may have for her.
One of the reasons that I would recommend a friendly call to begin with is that she is “so close” to whatever minimum requirement she missed – and obviously she did that in ignorance – so it may be possible to work around the minimum or waive it in this case. Most non-government agencies have a certain amount of leeway they can offer.
It would probably also be helpful if YOU can make the call on your mother’s behalf. That way you can help to keep emotion, recrimination, “you-should-have-told-her” and all of that kind of negative energy out of the conversation. People are a lot more willing to bend the rules for you if they figure that you’re all reasonable folks. If you start with threats, then they may be more likely to adhere to “exactly what the policy says”.
Some of the negotiating points that may work in your favor would be, for example, whether your mother can trade a paid vacation day or sick day – assuming she has any – to make up the shortfall.
In any case, once the conversation has been held, if you can’t get immediate relief, then at least you should have the information that you need to start an appeal.
Good luck!