A laundry washing machine having an outer casing, a washing tub, a rotatable drum, a detergent dispenser, a fresh-water supply circuit, an internal water softening device filled with a water softening agent capable of reducing the hardness degree of the fresh water directed towards the detergent dispenser or the washing tub, a regeneration-agent reservoir located/recessed inside the outer casing and structured for being manually fillable with consumable salt or other regeneration agent, a first water-supply line for channeling fresh water into said regeneration-agent reservoir so as to form brine, a brine reservoir fluidically connected to said regeneration-agent reservoir for receiving and accumulating the brine arriving from said regeneration-agent reservoir, and a detector assembly for detecting when the salinity degree of the brine stored into brine reservoir exceeds a predetermined minimum salinity value.