Hi,
you may try to rebuilt the link by investigating the Change document tables (CDHDR - CDPOS).
Of course this should be done with a report that may the save then value in the field you are currently using to save the link.
Access the CDPOS with objectclass = 'BELEGR' and in the objectid concaenta the year, number and company code (BKPF-GJAHR, BKPF-BELNR, BKPF-BUKRS but do not forget the leading zeros) of the invoice number: addFNAME = 'AUGBL' and CHNGIND = 'U' and start looking for the record where VALUE_NEW = ' ' and then check the VALUE_OLD number to be the payment (to have the complete key of the document, look for the records where FNAME contains AUGDT and AUGGJ).
I hope this is quite clear to you but I am sure your abapper may help you if the solution may be good for you.
Let us know!
Moody