This is kind of strange, it's the Fred Gambit which White could just accept.

You missed a chance for "en passant" lol

Well I'm pretty sure I would take checkmate over en passant

Where is the game and where is the annotation?

This is not Fools Mate. Fools Mate is another name for Scholars Mate, which involves Q + B on f7. This doesn't have a name, as Black (in this case) wouldn't fall for it unless deliberately trying to lose.

Fool's mate also refers to being checkmated in two moves because you have to play like a fool for it to happen. The earlier Black can checkmate white is on move 2 - however, the earliest White can get a checkmate is move 3. Thus, I guess this would be considered a Fool's mate too.

I thought fools mate was just moving your g and f pawns out to allow for mate with the queen.

@robyfish If I'm not mistaken, thereaper1 is right. This is the fool's mate (reversed, as White mates black in this case).

If this was a real game I believe black would've done this on purpose

This wasn't a real game. thereaper1 is correct: Fool's Mate and Scholar's Mate are quite different. I suppose the ironic appellation 'Scholar' might have to do with the fact there is some real chess involved in the latter, though both show up the vulnerablilty of the f2 and f7-squares, the only squares that are protected solely by the King. Scholars mate goes something like this: 1.e4 e5 2.Bc4 Bc5 3.Qh5 Nc6 (to protect the attacked e-pawn) 4.Qxf7#. But the thing can take many similar forms. Many players just past learning the moves like to bring the Q to h5 as early as move 2. Some bring the Queen out to f3 with much the same idea (1.e4 e5 2.Qf3 Napoleon's Opening). This attack is repulsed by 2...Nf6, but White can try Bc4 the redeploy the Queen to b3 to renew the attack on f7. But if Black has played ...Bc5 already, he can castle out of trouble, or simply ...Qe7 should keep his game intact.

This Mate does not even have a name! Call it Lastav's Mate.

It is lastav not Lastav.