You have it backwards. The recovery rebate credit is based on 2020. The checks that were issued last year were sent out n in a hurry so they used 2018 or 2019 returns----but the stimulus checks are an advance on a credit on 2020 tax returns. Someone who did not receive either the first or second stimulus check can get it on their 2020 tax returns IF they are eligible in 2020. A person being claimed as a dependent on someone else's 2020 tax return is not eligible. So if you claim him he does not get the $1200 , nor will he get the 3rd stimulus---which at this point has not even been passed.
Read the criteria to claim your BF and if he qualifies to be your dependent---you get a $500 credit for other dependents on your 2020 return. They will not award him a stimulus check based on 2019 now.
CREDIT FOR OTHER DEPENDENTS
https://ttlc.intuit.com/questions/4499708-what-is-the-500-credit-for-other-dependents-family-tax-cre...
https://ttlc.intuit.com/community/children-dependents/help/what-does-financially-support-another-per...
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