You are already on the right track with invoicing, but since you actually receive money against the invoices you need to receive payments, not credits. You could still create credits (to build before use) by receiving their collected funds as payments but not against any invoice - this creates a credit.

 But that calls for extra steps you may not need. You can identify the sponsored funds by adding a different and unique payment type. Maybe call it "Sponsor Pay" and this could envelope cash or check and you just deposit it as is.