[etni] bagrut without a tziyun shnati

I'm sure this question has been dealt with but...
I have a  4-point student in 12th grade who is doing module E next month but 
would like to make it up to  5-points  as soon as possible but without a tziyun 
shnati. That means (as far as I understand) that she'll have to do it externi . 
When is the earliest possible date that she'll be able to do that? She thinks 
that she could do F and G in moed beit. That's not the case, is it? She would 
need a tziyun shnati then, wouldn't she?
Next year she's doing national service. Will she be able to be tested in the 
winter as an externi student? If not, when is the earliest possible date?
Thank you in advance for your replies.
Rachelle Emanuel

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