SQLite 3.27

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create table purchases(id int, date date, purchase int);
insert into purchases values(1,	'2020-01',	200);
insert into purchases values(2,	'2020-12',	100);
insert into purchases values(2,	'2020-03',	150);
insert into purchases values(3,	'2020-03',	200);
insert into purchases values(1,	'2020-07',	120);
insert into purchases values(1,	'2020-08',	300);
insert into purchases values(3,	'2020-05',	250);
with cte as
( 
  select id,date,purchase,
  min(date)over(partition by id) FirstPurchaseMonth from purchases
)
,cte2 as
(
  select substr(date,6,2)-substr(firstpurchasemonth,6,2) Purchasemonth, max(FirstPurchaseMonth)firstpurchasemonth, 
  purchase,sum(purchase)total from cte
  group by firstpurchasemonth,substr(date,6,2)-substr(firstpurchasemonth,6,2) 
)
select purchasemonth,firstpurchasemonth,sum(total)over(partition by firstpurchasemonth order by purchasemonth)total
from cte2 


Purchasemonth
firstpurchasemonth
total


0
2020-01
200

6
2020-01
320

7
2020-01
620

0
2020-03
350

2
2020-03
600

9
2020-03
700

Purchasemonth	firstpurchasemonth	total
0	2020-01	200
6	2020-01	320
7	2020-01	620
0	2020-03	350
2	2020-03	600
9	2020-03	700