I am divorced with primary custody of my son. In 2019 my ex husband claimed him and therefore received both stimulus checks for child. Can the custodial parent get a tax credit for both checks?

[Hal_Al]

"In essence, the stimulus check acts as an advance of your 2020 income tax refund. This means when you prepare your 2020 income tax return, there will be a line to include the section 6428 credit. The credit on your 2020 return is subtracted by any amount received as a stimulus check in 2020. If the amount you received as a stimulus check is less than the credit you are due, the difference will be included as part of your 2020 refund. If you have been overpaid by receiving the stimulus check, however, you will not be required to return any excess amount".

That  says if, in the case of divorced or separated (including never married) parents, the other parent got $500 + $600 in 2020 (because he claimed the child on his 2019 return) you  also get it in 2021, if you claim the child on your 2020 return. It's a tax loop hole, you both get the money!  Be sure the ex doesn't try to claim the child on his 2020 return. 

[Hal_Al]

There is a way to split the tax benefits. For future negotiations with the other parent (and maybe even for this year) the following info may be of use:
This may be helpful in your negotiations with the ex:

 There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.

Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.

 So, it's good idea to let the other parent know that you will be claiming those items, as many first time divorced parents are not aware of this rule and may try to claim those items, which will cause the IRS to send out letters.

Ref: https://www.irs.gov/publications/p17#en_US_2017_publink1000170897

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