I'll try being more precise. My understanding is that the conditional expectation of a shock is always zero iff I'm integrating over the full distribution, that is from -inf to +inf. But if one integral's boundary is an endogenous variable, the expected value of the epsilon-shock shouldn't be zero. I think I can better explain myself if you have a look at the attached document from where it should be clearer what I would need to do.
Thank you for your time.