Get Last Value of previous row partition in SQL

In my data set, each customer has some orders on different dates.
For each customer each month, I want to check his/her last order in the previous month in which city.

For example, it is my data for one of the customers.

the result should be the same as this:

(the first row of the above table is not my question now. )
I write my query using last_value the same as this:

select customer,
   year,
   month,
   last_value(City) over (partition by customer, year, month order by created_at desc
       ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING) as prevCity 
 from table1

but the result is false!

How can I correct this?

>Solution :

Using the window function lag() over() in concert with the WITH TIES clause

Select top 1 with ties 
       customer
      ,year
      ,month
      ,LastCityID = lag([city id],1) over (partition by customer order by year, month,day) 
 From YourTable
 order by row_number() over (partition by customer,year,month order by year, month,day) 

Or an Nudge More Perforamt

with cte as (
Select *
      ,LastCityID = lag([city id],1) over (partition by customer order by year, month,day) 
      ,RN = row_number() over (partition by customer,year,month order by year, month,day) 
 From YourTable
)
Select customer
      ,year
      ,month
      ,LastCityID 
 From  cte
 Where RN =1 

Results

customer    year    month   LastCityID
1544        2022    2       NULL
1544        2022    3       10
1544        2022    5       21