Whenever I submitted my invoice's, the appropriate certification & notification had already been submitted to my client. I did so because of the advice given here on this forum by members (as it is in this thread).
However, I cannot find anything in BS7671 which states such documentation has to be provided, before payment. Not surprising really, as BS7671 is about requirements for electrical regulations, not good business practise.
Reg 631.1 Upon completion of the verification of a new installation...…, an EIC.…. shall be provided. So define completion?
Those who have bought & sold houses recently, could explain that you can't have your keys for the new house, until the solicitors have received the various monies.
I purchased a new build property, but never received the documentation, until well after moving in (in fact it had to go back, as it hadn't been signed).
I would say it is good practise to provided certification before receiving payment, but there is no requirement to do so.