Consequence of declining an accepted offer after the universal deadline 15th April
Assuming both schools are members of the Council of Graduate Schools, they have an agreement about cases like this. If you don't change your mind and reject the offer from the first school by April 15, you have to get a letter from the first school releasing you from your obligation to attend before accepting the second school. Otherwise, the second school will be unable to take you.

In the one case I know about, there wasn't any problem in obtaining this letter. However, I can't promise that all graduate schools will be as reasonable. 

If your cousin gets an offer from the second school before April 15, he should contact the admissions officers at the first school by April 15 (today!) and tell them he is rescinding his acceptance and why.

If he gets an offer after April 15, he needs to make sure the first school is okay with him not coming and get a letter from them before he accepts the second school.