Does your partner use MobileSheetsPro as well? If so, he could just export all of the songs with updated PDFs into one .msf, and you could import that and update all existing songs. If not, your best bet is to use the swap file feature with each individual song.
The other option would be to manage the files yourself instead of letting MS Pro do it, or just have your storage location be an easy to access folder on the SD card. Then, if a PDF needs to be updated, just drop the new version in the storage location, overwriting the existing file. MS will recognize that you changed the file and will update things accordingly.
The other option would be to manage the files yourself instead of letting MS Pro do it, or just have your storage location be an easy to access folder on the SD card. Then, if a PDF needs to be updated, just drop the new version in the storage location, overwriting the existing file. MS will recognize that you changed the file and will update things accordingly.