Both adding your own questions to someone else's discussion and resurrecting old threads is not allowed per SCN ROE.
But just to prevent someone else coming here with the same ridiculous requirement - there is no FM/BAPI because this is not supposed to be done. The partner determination occurs when the document is created. Normally, all the partners are copied to the billing document from the preceding documents. So if you want to have a partner in a billing document, it needs to be added before that - in the order or delivery. I suppose a partner can also be added when billing document is created, but I have not seen this so far.
Other that texts, billing documents are not supposed to be updated after the creation at all. Requirements like this usually indicate bad business practices or poorly designed SD implementation.