I have one table as below mysql

customer_id,invoice_id,invoice_month,payment_month,invoice_amount,payment_amt,balance_amt
1,1,"DEC 23","JAN 24",400.00,400.00,0.00
1,2,"DEC 23","JAN 24",600.00,600.00,0.00
1,3,"JAN 24","JAN 24",200.00,50.00,150.00
2,4,"SEP 23","MAY 24",800.00,800.00,0.00
2,5,"OCT 23","MAY 24",750.00,750.00,0.00
3,6,"FEB 24","MAY 24",925.00,525.00,400.00
4,7,"NOV 22","JUN 23",325.00,325.00,0.00
4,8,"DEC 22","JUN 23",425.00,425.00,0.00
5,9,"JUN 24",NULL,500.00,NULL,500.00

Payment table as

customer_id,payment_month,amount
1,JAN 24,500
1,FEB 24,550
2,MAR 24,450
2,APR 24,900
2,MAY 24,450
3,MAY 24,525
4,JUN 23,350
4,JUN 23,400

need to create a new columns payment_final_month based on “payment_month” from the payment table.
For the first record i have invoice amount has 400 which is less than the payment table amount first record then pick JAN 24
For the second record as i have 100 left from the first record then pick the same JAN 24
For 3rd record i should pick the FEB 24

Final output something as

customer_id invoice_id  invoice_month   payment_month   invoice_amount  payment_amt balance_amt payment_final_month
1   1   DEC 23  JAN 24  400.00  400.00  0.00    JAN 24
1   2   DEC 23  JAN 24  600.00  600.00  0.00    JAN 24
1   3   JAN 24  FEB 24  200.00  50.00   150.00  FEB 24
2   4   SEP 23  MAR 24  800.00  800.00  0.00    MAR 24
2   5   OCT 23  APR 24  750.00  750.00  0.00    APR 24
3   6   FEB 24  MAY 24  925.00  525.00  400.00  MAY 24
4   7   NOV 22  JUN 23  325.00  325.00  0.00    JUN 23
4   8   DEC 22  JUN 23  425.00  425.00  0.00    JUN 23
5   9   JUN 24  NULL    500.00  NULL    500.00  NULL

I tried below approach and didnt worked

i.invoice_amount - COALESCE(LAG(i.payment_amt, 1) OVER (PARTITION BY i.customer_id ORDER BY i.invoice_id), 0) AS remaining_amount