I'm not sure exactly what this query should be doing, but if you question is how to use insert with row_number then just do this:

INSERT INTO [ReceiptRepository].[Lkup].[BillingGroups]

select M.RowNum, M.BillingGroupNumber

from

(

select BillingGroupNumber, (row_number() over (order by BillingGroupNumber) - 1) % @Counter + 1 as RowNum

from Sap.DetailsImport

) as M

I'm not sure what the other variables are used for or why this is in a while loop.