if you’ve attached a PDF of the invoice to the email then obviously subsequent changes you make won’t affect the PDF
if the email you sent out included details of the invoice total and you make changes that change that total, you’re likely to raise eyebrows with the client when they see an email saying they owe X but then open the invoice and it states a different value Y
If the fix you want to make doesn’t change the invoice total (or the net/vat split if you’re VAT registered) then you’re probably safe to modify the invoice and hope the client doesn’t notice, but if you’d be changing the total or changing anything relating to VAT, or if the client has viewed the invoice before you get around to changing it, then you’d be safer cancelling the original invoice with a credit note and then issuing a new replacement invoice with the correct details. That way both you and they have the full audit trail and you can’t end up in a situation where you and your customer have different versions of an invoice with the same number.
No PDF attached so all ok there. It was a small mistake in the description of services provided, as said they haven’t logged in and viewed it yet so hopefully it should be ok if it automatically updates.