If for example, you want to issue an invoice for a membership that takes place in July, but want the period of the invoice to be in June, you can set the billing period of the invoice to June.
You can issue an invoice for a member/company by visiting their profile and clicking "Add invoice".
Initially, the Add invoice window will be empty, if everything has been invoiced for the month, however, you can use the Pay For as an option to select for how many months ahead you'd like to issue an invoice.
If you select Pay For 2 months you'll be able to invoice July memberships, while the period of the invoice remains in June.
If there are some items from July that you don't want to invoice you can simply de-select them using the checkboxes before the line items.