is the apostrophe ( ' ) really a part of your 1st sentence? well, if it is then you are implying that you're going to send someone either the duplicate or photocopy of the invoice, while the 2nd sentence may imply that you're going to send someone the real/genuine/original invoice......~lol.. to remake the 2nd sentence: I'm going to send you the copy of the invoice. (please take note the the word 'copy' here acts as a measure word. Thus, you may omit the word 'copy', giving you: " I'm going to send you the invoice.")

If you want to use 'send' then "I will send you a copy of the invoice" works better. If not try, "I sent you a copy of the invoice" if you want to say it's on the way.

I'll send you a copy of the invoice.

I guess is the second