It is always a good idea to continue with his schooling so that his F-1 visa remains valid until you are certain that you have properly filed his green card application and have a receipt as proof that it has been received by the USCIS. This applies to all types of visas too. It is always best to maintain your current visa until you actually make the transfer, just in case something goes wrong.
For legal advice regarding your case you should consult an attorney as this is information of a general nature and not intended to be legal advice.
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