The HCl salt won't dissolve in much. You would need to make the free base to dissolve it in organic solvent, or buffer the reaction. But with an Fmoc, that is tough.
You could try Shotteb-Baumann conditions, they work fine for that reaction, using the chloroacetyl chloride. See Vogel for an example. That involves aqueous NaHCO3 and an organic solvent like THF or even DCM. That keeps the Fmoc group in the unbasic organic solvent, but neutrallizes the HCl from the SM and the reaction.