Overstays are noted against application and overstays of greater than about a month are noted when the person leaves the UK to go back home. If you son has evidence that he has been waiting for admission to another university then he should take this with him when he returns home.
They may pick up on the overstay when he makes a further application, they may not bu their objection to the overstay will grow the longer your son stays here without leave to remain. He should return home and make an application from there.
The overstay is not yet of a length that cannot be reasonably explained (eg. waiting for college admission, arranging flights, making other practical arrangements to return home, waiting for you to arrange his return for whatever reason (eg. lack of funds) but, as I say the longer this overstay continues the more prejudicial it will be to his next application.
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If he does not include reference to the overstay in his new application then the UKBA may view that as dishonest which could be more damaging to the application than the overstay itself. The better view is to be honest and pre-empt by offering the most cogent explanation for it that he can. A relatively short overstay of this type is quite explainable.
There is no time limit within which he must apply for further student visa.
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