How would 2-(chloromethyl)-1-methylpyrrolidine recyclize into 3-chloro-1-methylpiperidine with only water?
Forget about the water present - its just a solvent.
The best nucleophile present is the N-lone pair; if you think about it in 3-D you will see that it can do a nucleophile attack on the CH2-Cl to displace Cl- and form the aziridinium cation. Cl- can then attack this at either carbon of the [3] ring, one attack merely reforms starting material, the other gives the 3-Cl-piperidine product shown.