How do I do this?

You can't, AFAIK. That's the difference between setting 'Ally' and 'Team' status at the game's start--alliances can be broken, teams can't.

Sooo... I can't win, because at the beginning I set the game up so I could only have a conquest victory?

I can't win

seems not.

Try to culture flip their planets. That is the only way you can win at this point. If one of their planets have a re-education center, try to trade for it. If need be, offer them plenty of planets that don't have a re-education center.

"because at the beginning I set the game up so I could only have a conquest victory"

So an influence victory won't work either. He has to invade that last planet, which he can not do as long as he is still part of a Team.

Does the random event where the other leader is killed have any effect on a team?
I seem to remember that happening to me once when I was teamed with the Terrans.
(But it may have only been an alliance, I can't remember)

If so, the game could be played until that point because the new leader always declares war.

It might be a long time coming, though.

I never said "Influence victory". What I said was "Culture flip". That means, you spam influence until planets revolt to your side. Once a civilization has no more planets, it loses. When there no other civilizations, you win a conquest victory. This occurs, even if you did so by spamming influence.

Don't think I don't know what I'm talking about. I did a quick test a few minutes ago. I used a tiny galaxy, and set the AIs to drool mode. I then spammed influence until all of the other races planets culture fliped to my civilization, including my team member. I then won a conquest victory.

OK, thanks for clearing that up.

You're welcome.

I always thought that you didn't need to finish off your team-mates. Are they the only ones left, other than you?

Wuth the OP's initial settings he will have to flip all of the AI planets to get a win.