"I was planning to report his 2020 tax return as normal, and amend his 2020 tax return after he completed all the repayment. If this is not the best way, please kindly share."

You would file by Year of the event(s).

Pub 525 tells you: Repaid social security benefits. If you repaid social security or equivalent railroad retirement benefits, see Pub. 915.

If he made repayments in 2020, against 2020 benefit payments, Pub 17 tells you to Net 2020 SS (gross received minus repaid). There should be a SSA-1099 for 2020 already with this info on it. You don’t Amend 2020 to include 2021 repayments. The 2021 SSA-1099 will show the repayment amount as negative benefits.

For the year with only repayments, you’ll be following the Repayment computation (Pub 17, 525 both have it), read this part:

“Repayment of benefits received in an earlier year.

If the total amount shown in box 5 of all of your Forms SSA-1099 and RRB-1099 is a negative figure, you may be able to deduct part of this negative figure that represents benefits you included in gross income in an earlier year if the figure is more than $3,000. If the figure is $3,000 or less, it is a miscellaneous itemized deduction and can no longer be deducted.

Deduction more than $3,000.

If this deduction is more than $3,000, you should figure your tax two ways.”