Hi.
Your ex is wrong. If you have a joint mortgage, you are both individually legally contracted to pay the mortgage whether living there on not.
If your ex does not pay, his credit rating will be damaged and he will find it harder & moe expensive to get a mortgage, credit card or tenancy in future
Any other bill that is in his name and is not paid, will further impact his credit limit, making his future finances very difficult. Can you point this out to him. Or get someone else to.