If you're like most freelancers, and have a handful of clients or less, then you likely have a pretty keen sense of who has paid you vs. what is still outstanding. Receivables are a source of much anxiety for the self-employed.
So, assuming you got paid for the work, then all of your recent bank deposits – except for one! – should match up with a recent invoice. That unmatched bank deposit should correspond to the missing invoice.
Your bank statement (or a print screen) showing the specific deposit that went into your account is already proof that you received the revenue. As long as you declare this revenue on your taxes, you should be in the clear. On a paper copy of the statement, circle the deposit, add a note, and file it with your other invoice copies. FWIW, any decent tax accountant should want to reconcile your invoices with your bank deposits, anyway, in order to discover potentially missed revenue.
You could also reverse-engineer a new invoice based on that amount, using the invoice template you originally used. Mark the "new" copy of the invoice as a "duplicate - original lost". Write a brief note explaining the problem. I would expect that as long as the amount and client billed are correct (and you said you already know who the client is), and the invoice date is within reason (i.e. within the same reporting period as originally invoiced, not necessarily the same period as when you received the revenue), then there's nothing sinister in doing this.
The kinds of paperwork that the tax authorities really want you to have originals for are your expenses, because you will deduct expenses from your taxable income and reduce your tax liability. Usually a tax authority won't challenge your paperwork when you declare additional revenue, because that increases your tax liability.
Run this by your tax accountant if you're still concerned.
(p.s. my answer is based on my own experience here in Canada – and I notice you're here, too.)
I certainly understand income implies sales taxes. If the OP knows the amount received, and that amount included the GST/HST, then in reverse-engineering the invoice as I suggested, he'd calculate the amount of GST/HST included in the total and account for it when remitting his GST/HST filing. FWIW, Canada (I and the OP are located here) isn't as high on ceremony. (Yet, one tracked & numbered form I've come across here that is issued by our government for use by business is the Record of Employment (ROE) -- the special treatment is because it can be used to claim unemployment benefits.)