To get better help, it would also be useful to explain why it's an issue if
the client modifies the invoice.
Suppose you bill the client for $1000, makes no changes to the invoice, but
pays you only $800. I expect you would still keep track of the fact that he
owes you $200.
Doesn't the same procedure apply whether he modified the invoice or not?
Surely he's not able to modify your copy of the invoice.