A solution using analytical function max() over(order by). This looks at all the available dates for an institution and generates 12 rows one for each month. I have slightly modified the input DML statements to test various scenarios. More complicated than the earlier solutions i guess but made more generic


CREATE TABLE data
(
  ReportingMonth datetime,
  Institution varchar(4),
  Totals integer
);
GO

INSERT INTO data
VALUES
('2018-01-01','Ins1',32),
('2018-02-01','Ins1',37),
('2018-03-01','Ins1',32),
('2018-04-01','Ins1',40),
('2018-05-01','Ins1',38),
('2018-06-01','Ins1',37),
('2018-09-01','Ins1',40),
('2019-09-01','Ins1',42),
('2018-01-01','Ins2',145),
('2018-02-01','Ins2',155),
('2018-01-01','Ins3',1489),
('2018-02-01','Ins3',1487),
('2018-03-01','Ins3',1485);
GO

with generate_12_months
as (
   select dateadd(month
                  ,y.rnk-1
                  ,cast(concat(year_val,'-','01','-','01') as date)
                 ) as running_months
          ,x.institution 
      from (select top 12
                   row_number() over(order by (select null)) as rnk
              from sys.objects
            )y
       join (select distinct /* for each distinct year in a institution generates 12 months*/
                    datepart(year,reportingmonth) as year_val
                    ,Institution
                from data
             )x
           on 1=1
    )
,interim_data
 as (
     select cd.running_months
            ,cd.institution
            ,d.totals
            ,d.reportingmonth        
        from generate_12_months cd
   left join data d
          on cd.running_months=d.reportingmonth
         and cd.institution=d.institution
      )
,interim_data2
  as(/*the max reportingmonth gets the first not null value of the month ordered by running_months*/
     select *
            ,max(x.reportingmonth) over(partition by x.institution order by x.running_months) as max_val
       from interim_data x
      )
select *
       ,max(y.totals) over(partition by y.institution,y.max_val) as not_null_totals
  from interim_data2 y