I have the feeling that it was Snape, disguised as Lupin, who showed up in 12 Grimmauld Place in the chapter The Bribe in the last Harry Potter book. Supporting evidence for the claim:
- Snape already knows the information Lupin gives Harry to recognize him. It is also so-Snape-ish to quickly blame Hermione and Ron for lowering their defense too soon.
- Lupin had already given up directly helping them on Dumbledore's mission. It is also not in Lupin's character to leave the wife and the baby during this time given we know him in the books as a less adventurous person compared to James and Black. After all, what was Lupin's business to endanger himself and show up there?
- When Harry meets Lupin at Bill's place, he acts as if it had never happened.
- We know Snape could bypass the protection set by Mad-Eye. The Chapter The Prince's Tale reveals he could actually be there.
- Snape had shown the desire in his memories to know about Harry's mission set by Dumbledore. Maybe he thinks he can help and that's why he is insisting to join them.