Your client is eligible to get the payment. Here is info from IRS:

This is link: https://www.irs.gov/newsroom/why-the-economic-impact-payment-amount-could-be-different-than-anticipa...

Parents who are not married to each other and do not file a joint return cannot both claim their qualifying child as a dependent. The parent who claimed their child on their 2019 return may have received an additional Economic Impact Payment for their qualifying child. When the parent who did not receive an additional payment files their 2020 tax return next year, they may be able to claim up to an additional $500 per-child amount on that return if they qualify to claim the child as their qualifying child for 2020.