MySQL 5.6

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Records: 2  Duplicates: 0  Warnings: 0

id	datefrom	datetill	amount
1	2020-01-10	2020-02-15	1000.00
2	2019-01-10	2020-02-15	1000.00

SELECT id,
       datefrom,
       datetill,
       amount,
       monthstart,
       monthfinish,
       amount * (DATEDIFF(LEAST(datetill, monthfinish), GREATEST(datefrom, monthstart)) + 1) / (DATEDIFF(datetill, datefrom) + 1) monthamount
FROM ( SELECT test.*,
              (test.datefrom - INTERVAL DAY(test.datefrom) - 1 DAY) + INTERVAL numbers.num MONTH monthstart,
              LAST_DAY((test.datefrom - INTERVAL DAY(test.datefrom) - 1 DAY) + INTERVAL numbers.num MONTH) monthfinish
       FROM test
       JOIN ( SELECT t1.num*10+t2.num num
              FROM (SELECT 0 num UNION SELECT 1 UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9) t1
              JOIN (SELECT 0 num UNION SELECT 1 UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9) t2
            ) numbers
       HAVING monthstart <= test.datetill
          AND monthfinish >= test.datefrom
     ) subquery
ORDER BY id, monthstart;

id	datefrom	datetill	amount	monthstart	monthfinish	monthamount
1	2020-01-10	2020-02-15	1000.00	2020-01-01	2020-01-31	594.594595
1	2020-01-10	2020-02-15	1000.00	2020-02-01	2020-02-29	405.405405
2	2019-01-10	2020-02-15	1000.00	2019-01-01	2019-01-31	54.726368
2	2019-01-10	2020-02-15	1000.00	2019-02-01	2019-02-28	69.651741
2	2019-01-10	2020-02-15	1000.00	2019-03-01	2019-03-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2019-04-01	2019-04-30	74.626866
2	2019-01-10	2020-02-15	1000.00	2019-05-01	2019-05-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2019-06-01	2019-06-30	74.626866
2	2019-01-10	2020-02-15	1000.00	2019-07-01	2019-07-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2019-08-01	2019-08-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2019-09-01	2019-09-30	74.626866
2	2019-01-10	2020-02-15	1000.00	2019-10-01	2019-10-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2019-11-01	2019-11-30	74.626866
2	2019-01-10	2020-02-15	1000.00	2019-12-01	2019-12-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2020-01-01	2020-01-31	77.114428
2	2019-01-10	2020-02-15	1000.00	2020-02-01	2020-02-29	37.313433