prepayment invoice
advance payment invoice
advance invoice

Note that to avoid confusion I've labeled the new invoice as the "Prepayment Invoice" to distinguish it from the "Normal Invoice" we send out later and which we'll use as the true up mechanism.

These are 'advance invoices' and must be in sterling for VAT purposes.

During the expenses scandal, several MPs including Alistair Darling, the chancellor, had to repay money after submitting advance invoices and then “flipping” their designated second home.