Yes, incarcerated people are eligible for the stimulus payments.
To obtain his stimulus payments, he has to file a 2020 tax return.
The following is for him:
Even if you did not have any income in 2020, you can use the IRS Free File Program by TurboTax to prepare and e-file your tax return in order to claim the stimulus payments known as the Recovery Rebate credit. The federal return will file as usual and will not be rejected. Any state return should be removed, as there will not be a state filing requirement.