According to the Noether theorem, we only have the conserved quantity $$J+S,$$ where $J$ is the orbital angular momentum and $S$ is the spin angular momentum. But I am always impressed that the spin is a conserved quantity such as in the case of EPR paradox. One may think that in the EPR paradox, we only deal with non-relativistic system and spin $S$ decouples from angular momentum $J$. But even in QFT, spin is always used to characterize the particle state and so is also treated as conserved quantity.
Could you please point out what did I miss in the analysis?