I always found the change of measure as given by :
The radon nikodym derivative with $Q$ and $P$ the probability measures :
$$Z=\frac{dQ}{dP}$$
The change of measure :
$$E^P[X]=E^Q[XZ]$$
My question is : If I have to compute a conditional expectation instead, would this be true ? :
$$E^P \left[ X|F(s) \right] = E^Q[XZ(s)|F(s)]$$
If it is, how can I get this formula from the first one? Thank you in advance.
No… you have to use the Bayes formula for conditional expectations.
You also find the proof of it as an answer if you follow the link.