In order to see which adoptions are included in a monthly billing invoice, you'll want to use a Custom Events Accounting Report. A standard outcome report cannot be used since adoption events are able to be back dated.

Once you have run the Custom Events Accounting report for your desired date range, export the report to Excel and apply a filter to the Item Name column. Filter for rows beginning with 'Adopted:' and select all results in the search. This will provide you a list of all adoption transactions for the month that were included in your monthly invoice.