How to replace null value with value from the next row

You can try below sql code using co-related subquery

SELECT v1.r#,CASE WHEN value IS NOT NULL THEN v1.Value     
             ELSE ( SELECT TOP 1 value
                    FROM @value  v2
                    WHERE v2.r# > v1.r# AND v2.[value] IS NOT NULL
                  ) END  Value 
FROM @value v1

OR (without Case statement)

SELECT v1.r#,ISNULL(v1.VALUE,( SELECT TOP 1 value
                            FROM @value  v2
                            WHERE v2.r# > v1.r# 
                            AND v2.[value] IS NOT NULL
                           ) 
                      ) AS [MonthNames]
FROM @value v1

Result

r#  Value
----------
1   January
2   January
3   February
4   March
5   March
6   December
7   December
8   December
9   November
10  November
11  November
12  November
13  NULL

Next approach may help. You need additional APPLY operator to find the first record with not NULL value:

T-SQL:

SELECT v1.[r#], COALESCE(v1.[value], v2.[value]) AS [value]
FROM @value v1
OUTER APPLY (
   SELECT TOP 1 [Value]
   FROM @value 
   WHERE (v1.[r#] < [r#]) AND [value] IS NOT NULL
) v2

Output:

r#  value
1   January
2   January
3   February
4   March
5   March
6   December
7   December
8   December
9   November
10  November
11  November
12  November
13  NULL

You can do this with window functions. Unfortunately, SQL Server doesn't support the IGNORE NULLs option on LEAD(), so that is not an option.

However, you can use two levels of window functions:

select v.r#, v.value,
       coalesce(v.value, max(value) over (partition by next_r#)) as imputed_value
from (select v.*,
             min(case when value is not null then r# end) over (order by r# desc) as next_r#
      from @value v
     ) v
order by v.r#;

On 13 rows, the performance difference is probably not noticeable. However, this should have much better performance as the number of rows increases.

below query works in SQL Server:

;WITH CTE_Value
AS (
    SELECT R#, Value
    FROM @value AS T
    WHERE Value IS NOT NULL

    UNION ALL

    SELECT t.r#, c.Value
    FROM @value AS t
    INNER JOIN CTE_Value AS c ON t.r# + 1 = c.r#
    WHERE t.Value IS NULL
    )
SELECT *
FROM CTE_Value

UNION ALL

SELECT v.*
FROM @value AS v
LEFT JOIN CTE_value AS c ON v.r# = c.r#
WHERE c.r# IS NULL
ORDER BY r#