"And the new broker won't issue a 1099 for the conversion in 2021 since it was put directly into a Roth a/c."

It would be because this new Broker had nothing to do with the Outflow. They would be the one issuing a Form 5498. Not any 1099-R. They would only issue a 1099-R if it had gone first to a Trad IRA, then converted to inhouse Roth account.

The IRS will have 2020 1099-R, so that is the one you would address. And since the "check was late" in arriving in 2021, I would keep any info that proves there was intent to make this a timely conversion, and why it didn't happened timely was not under the taxpayer's control (they didn't delay on a rollover so they could use the money in between, for instance).