Can he just add the loss carryforward from 2019 to his 2021 Schedule E?

Are you talking about a "Passive Loss Carryforward".

I would probably prepare and file the 2019 return, then update the 2020 return for the carryover, If there is no tax affect I might just keep a copy of the relevant changed forms in the file, rather than amending 2020 if there is no tax affect., and update the passive carryover schedule to reconcile into 2021.

But I have to be honest, Amending 2020 or just changing the schedule, That answer would probably change from day to day.