I am now divorced this year and filing head of household, my ex has filed separate and claimed all 3 children. I personally never got the stimulus, she took it all but IRS is stating I received it. She didn't work hardly last year but I worked all year and paid for all the medical, housing and for the kids.
First of all, if you are not claiming any dependents, you can't file as head of Household.
Since the IRS sent the payments based on your 2020 tax return, the IRS will consider those payments as received by you both. The IRS records show you received half and if you claim zero (0), your return will be delayed.
If you claim the amount the IRS has on record, you may be eligible for "Repayment Protection" in which case you won't be penalized for the payments.
According to the IRS:
"You won’t qualify for any repayment protection if your modified adjusted gross income (AGI) is at or above the following amount based on the filing status on your 2021 tax return:
If you would be penalized for the payments that you say you never received, you would have a difficult time with tracking payments and proving the funds were received by your ex, without your knowledge, and that you reported your life changes using the IRS website. It could be done, but most likely would involve the courts.
Hopefully, claiming the payments will not create a tax liability for you.
who is the true custodian of the children ?
If it is you then the IRS will contact one or both of you to find out who is really entitled to claim dependents.
Presumably the issue of which parent claims which child(ren) was settled in the divorce filings. I would expect the courts would have allowed each parent at least one child so both could file HoH. Check with your attorney on this if you can't find it in the paperwork yourself.