Can I take a water softener with me when I move?

Most certainly, this is possible with modern softeners. Installation techniques involve quick fitting connections, similar to those used with washing machines. All that is necessary, is to close off the inlet and outlet valves to the softener and open up the bypass valve, allowing hard water to flow to the storage tank and household taps. The softener can then simply be disconnected, moved to its new location and replumbed as necessary.