After you file

I am the custodial parent and I have sole legal sole physical custody of a child, the other party did file taxes for 2019 but lied and use my address and also maybe claiming head of household where I live.our child has never once stayed over his house,a he may have seen her three to four times from last year until now. IoI my house and that person has not been here for a couple of years. He has his own residence and also put a photo ID in my address without asking me, so he can use it for IRS. 2018 he was not living at my address either and when updating the photo ID he failed to use his proper address and used mine. The stimulus check came here not too long ago that's how I found out he's using my address and I sent it back to the IRS stating he has not lived here for a couple of years. He did try to file 2019 and claim my child but I filed first and he called me yelling that's how I know. But I didn't know that he was using and claiming my address which means he has to claim head of household to claim her and get all the tax credits. I just do not want him to be able to use my address and falsifying info. What can I do?