Calculating calendar weeks from fiscal weeks

Question

So I am really new to this and struggling with something, which I feel should be quite simple.

I have a Pandas Dataframe containing two columns: Fiscal Week (str) and Amount sold (int).

	Fiscal Week	Amount sold
0	2019031	24
1	2019041	47
2	2019221	34
3	2019231	46
4	2019241	35

My problem is the fiscal week column. It contains strings which describe the fiscal year and week . The fiscal year for this purpose starts on October 1st and ends on September 30th. So basically, 2019031 is the Monday (the 1 at the end) of the third week of October 2019. And 2019221 would be the 2nd week of March 2020. The issue is that I want to turn this data into timeseries later. But I can't do that with the data in string format - I need it to be in date time format.

I actually added the 1s at the end of all these strings using

df['Fiscal Week']= df['Fiscal Week'].map('{}1'.format)

so that I can then turn it into a proper date:

df['Fiscal Week'] = pd.to_datetime(df['Fiscal Week'], format="%Y%W%w")

as I couldn't figure out how to do it with just the weeks and no day defined. This, of course, returns the following:

	Fiscal Week	Amount sold
0	2019-01-21	24
1	2019-01-28	47
2	2019-06-03	34
3	2019-06-10	46
4	2019-06-17	35

As expected, this is clearly not what I need, as according to the definition of the fiscal year week 1 is not January at all but rather October.

Is there some simple solution to get the dates to what they are actually supposed to be?

Ideally I would like the final format to be e.g. 2019-03 for the first entry. So basically exactly like the string but in some kind of date format, that I can then work with later on. Alternatively, calendar weeks would also be fine.