Now, show use what you have tried to solve your problem. 
Also, the following is a much better way to post the DDL, sample data, and expected results, which I...

Now, show use what you have tried to solve your problem. 
Also, the following is a much better way to post the DDL, sample data, and expected results, which I...

It may still need some more work as it isn't fully tested against all possible scenarios of data.

Sort of like this:

create table [dbo].[mytable]
(
[StartDate] date not null primary key
, [CalendarMonth] as datepart(month,[StartDate]) persisted
, [CalendarYear] ...

Also, you really shouldn't be using a loop for this.  You could put this into the table from your other thread.

It probably needs some additional work but I will leave that to you to at least attempt first.  Questions or problems please come back here.

Here is a partial solution.  It doesn't incorporate the WHERE clause for the time sheet information.

/****************************************************************************************
Generate employee data
****************************************************************************************/
if object_id('[dbo].[Employee]','U') is not null
...

Use the table in your other thread here, https://www.sqlservercentral.com/Forums/2008707/get-qtrmonth-and-year-from-start-date?Update=1#bm2008841, using the [fy_year] and [fy_month] columns to create the YYYY-MM, like this:
CAST([fy_month] as varchar(4)) + '-' + right('0' + cast([fy_month] as...

Just one thing missing, to get the expected results how is the query run.  I am trying to figure out how the employees come together using the start and end...