Thanks for your question.
If it is the case that she has worked at one of those forms of institutions then you should answer yes. Deception is taken very seriously by the UKBA and is a general ground for refusal, depending on how material the deception was.
If you made an honest mistake in not ticking "yes" on the original form because you misunderstood the question then you should explain this to them in your statements. Simply state that it was a misunderstanding of the question being asked and having gone through the questions in more detail after receiving your rejection initially you became aware of the question being asked. Impress upon them that this was simply a case of honest mistake and was in now way an intentional deception.
You will have to provide as much detail about the job as you can, together with the letter, and also that there was no formal contract of employment. Explain that this is common place in Nigeria, they appreciate that other countries do not have the employment infrastructure that we do and do not have a wealth of documentary evidence supporting the existence of the job.
Provided you follow the above you should be fine.
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