Well, when you say "Turbo Tax" do you mean that Turbo Tax informed him that his e-file return was rejected by the IRS for that reason, that someone else claimed that dependent?
If so, does he know or can he determine from talking to his ex-wife whether or not she claimed the child?
I ask, because of all the identify theft, the number could have been used by someone else.
If that's not possible & he wants to presume that his ex-wife did claim the child, all he can do now, is to file a paper return claiming the child, with a copy of the divorce agreement and a "Statement, made under penalties of perjury, that 2015 was his year to claim the child", & attach it to the face of the return.
The IRS will sort it out and send her an adjustment disallowing the child as an exemption, and accept his return as filed.
The only other alternative is to get her to amend her return to remove the child as an dependent and inform her that if she doesn't the IRS will make the adjustment and she will be subject to penalties & interest.
The IRS will review the situation