Without an A1 pass, the application would have been rejected anyway, irrespective of the application date. There are no possible grounds for appeal, since it is an absolute requirement that the A1 test has been passed, unless the applicant falls within one of the exemptions.
Assuming the applicant is not exempt from the A1 test, she needs to consider what application needs to be made, in order to stay in the country, take the A1 test and then submit a new application for ILR. For that, I would suggest she now needs legal assistance from someone properly qualified.
If the applicant is exempt from the test on the grounds of a qualification equivalent to a UK Bachelors Degee, that was taught in English, she could obtain proof of this from NARIC but she would still have to submit a new ILR as she did not provide proof of exemption with the initial ILR application; it may be simpler just to take the test anyway. In the meantime, she would still probably have to apply for FLR again until she was in a position to re-apply for ILR.