Your son received the third stimulus because he is eligible for it.
You received the third stimulus for him because the IRS based the amount on your 2019 tax return where he was your dependent.
In this case, you can both keep the stimulus payment and nobody has to repay it.
The IRS says in this document:
If a taxpayer's payment is less than the full amount and is based on their 2019 return, they may qualify for a supplemental payment after they file their 2020 return. The IRS will automatically reevaluate their eligibility. If the agency determines that they are entitled to a larger payment or the full payment, it will send them a supplemental payment covering the difference between what they originally received and the larger amount. If the re-evaluated amount is smaller, they won't need to pay back the difference. Aside from filing a 2020 tax return, no action is needed on their part.
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