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What does the reconsideration say?
Have you received a decision yet?
I am confused. Have you received any decision?
I need to understand your situation better. Could you give a time line of events?
In the refusal does it say you can request a reconsideration or does it say you can appeal?
So you cannot simply ask for reconsideration. So any reconsideration letter is ignored and has no legal force. A regulated immigration solicitor cannot have told you to write a letter for reconsideration when the only option is to appeal.
If in your letter of refusal there is no option for a reconsideration, you CANNOT ask for a reconsideration. In the link you sent they would have been given the option for a reconsideration. That is why my first question to you was whether you were given one.
You cannot simply use support given in other cases to make decisions about other cases because each case is different.
They made their application abroad but you made yours in country.
No because they have already written to you in the refusal saying you can only appeal.
and the appeal option has a deadline.
I am afraid the only practical options you have is to seek face to face legal advice or make a fresh application.
Unfortunately the facts you have presented are incomplete and makes no sense to me at all. If her application was rejected based on suitability then there is more to this refusal because the suitability requirements covers issues to do with criminality, deception and owing money to the NHS etc
I can only suggest making a fresh application.