"There's no 1099-R, was he supposed to get one?"

Yes. 1099-R is for money Out. Are you sure it isn't available from the account brokerage or financial institution, such as from online? He might not know he needs to "go get it."

A conversion is the same as Distribution + Rollover, but the change in nature of account is why it's called Conversion.

BackDoor simply means: Basis in a sheltered account is moved to a tax exempt account quickly enough that there are no earnings or any deferred amounts that need to be taxed.

If they had any funds other than Basis in that Trad IRA account( or any of the similar account types as listed by the IRS), then this is not BackDoor, but a Partially Taxable conversion.

You stated "in 2020." Does this means they made a nondeductible contribution and converted it all in 2020? Or, are you describing they made the contributions for 2020 but in 2021 and then converted it, which means the 1099-R won't be out until 2021.

You would still prepare form 8606 and enter that this was Basis. A lot of people forget Basis on the 8606.