your chances are extremely slim. Modern file systems like NTFS, HFS+, ext3, and reiser all use meta data for their files. You see before meta data was around and you modified a file, like for example, changed the date on it; it would actually make a whole new copy of the file and mark the old one for deletion when the space was needed. That caused a lot of fragmentation issues. These days that is no longer the case. Every time you modify a file it overwrites the existing file and all the data about your data is stored in the meta data. And of course you are able to even edit the meta data as well.
The only thing you may be able to salvage is the creation date of the invoice, but again that does not prove anything. I also work as an independent/sub contractor for onsite technology. My invoice template was created over a year ago, so every single invoice I make using MS word, all have the same creation date. This is because I made a template where i could just fill in the blanks. I can only assume anyone who is writing invoices would do this, it makes much more sense than recreating the file every time you needed to send out an invoice.
I wouldn't bother trying to prove this unless you really are willing to spend the 1000s upon 1000s of dollars it costs to do a complete data salvage from a HD. Which would require having the physical disk and destroying it. The machinery they use will destroy the HD during the process. Or if this person actually kept the original invoices and the modified ones. However, you won't know until you have physical access. Also be careful because if you use any unlawful methods to obtain this data it will be totally inadmissible in court.