Why is 'He won't forget it if he is rich' incorrect?

Question

What I've learned about conditional sentences is when we have will, it must be the first kind of conditional sentences (type I).

But, take a look at this

Who's wrong? The app or I? It's an app called English Grammar and Test, by the way. I would use wouldn't instead of won't. I've heard something about mixed conditional sentences, but I believe there are only two cases:

1. If (past perfect tense), (would + present tense)
2. If (past tense), (past perfect tense)

Are there other mixed conditional sentences that I haven't encountered?

Answer 1

I'd use "is". The I II III system of conditional sentences is a simplification for learners, and it is easy to find examples that don't fit these.

Here the sentence is weird (what does being rich have to do with remembering things?) but I'd expect "He wouldn't forget it if he were rich" or "... wouldn't have forgotten...were..." for the hypothetical. Or "He won't forget it if he is rich" for the conditional about a future event.