Is it possible to tie a PO to a CPA after it has been invoiced?

Is it possible to tie a PO to a CPA after invoicing? Our client has POs that were not tied to their corresponding CPAs at the time of creation, but they need to link them. Previously, we had them duplicate the line, then zero out line 1 and add the $ and CPA to line 2, but that only works if the PO has not been invoiced. Does anyone have any suggestions on a feasible workaround if the PO has been fully invoiced/paid, but it needs to be tied to a CPA?