Several issues here. First, he can't say that he can't be claimed by someone else since he clearly can be. Second, you say that your ex wife is filing married, filing seperately, but she can't do that if you're divorced. If she was the one eligible to claim him as a dependent, but chooses not to, then you should get a letter from her to that effect, and then you may claim him as a dependent since he lived with you and you provided more than half of his support.
See the following: https://turbotax.intuit.com/tax-tips/family/rules-for-claiming-a-dependent-on-your-tax-return/L8LODb...
Answers are correct to the best of my ability but do not constitute legal or tax advice.
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