The money would be part of his estate, and would go to his heirs. The procedure for this will depend on whether he had a Will and the laws of the state he lived in. It will not have to be returned.
technically, the stimulus payment is in advance on a new credit that will be part of the 2020 tax return. The IRS is issuing payments now using 2018 and 2019 information to get them out faster. The credit will be recalculated on the 2020 tax return. If a larger credit is due some taxpayers at that time, it will be added to their refund. If a smaller or no credit is due, taxpayers will not have to pay it back.
If your father-in-law had taxable income during 2020 before he passed, someone will still need to file a final return for him. If any taxes are owed next year, it will be the responsibility of the executor of his estate to see the taxes paid before his remaining assets are distributed to his heirs. So bear this in mind.
