Combine and rearrange the neutralization of HCl by NH3 and the dissolution of NH4Cl in water to arrive at the decomposition of NH4Cl?

Question

I know the eq. is NH4Cl -> NH3(g)+HCl(g)
But I am confused how this works with the decomposition of H2O?
Here is what I have so far:
NH3(g) ----> NH3(aq)

HCl(g) ----> HCl(aq)

HCl (aq) + NH3(aq) ---> NH4Cl(aq)

NH4Cl (aq) --> NH4Cl (s)

NH3 (g) + HCl(g) ----> NH4Cl(s)

NH4Cl(s) ----> NH3 (g) + HCl(g)