I’m sorry. Being too imprecise here. You do know how 8332 works, so that’s a huge benefit. The question here are what do you net gain by letting your Ex declare your sin as depended is 8332? I use “you” including your son.
When your son chooses his school with his scholarship package, it may involve some planning to get the most out of the tax laws, looking at credits and deductions involved. If your ex can benefit from the AOTC and will give you that tax credit refund back, it could be worth while doing. But if your son gets a full ride, it might take some creativity, as he will have to declare room, board expenses as income. For 2020 less likely to be an issue as only one semester could be involved but it can get more complicated as the amount (often with summer and part time job earnings) turns into taxable income. It could be beneficial for you to pay a certain amount of his colleges expenses, in order to get that AOTC if Ex is willing to send the money to you when he gets it.
It can get to be tricky with 529, possibility of independent student, tax credits , HOH status, all or in part in the picture to end up getting g the most benefit net. Your particular situations will direct the best path to that.