Nozzle assembly of a fuel injector comprising a body having a peripheral wall defining an inner space wherein is guided a valve assembly comprising a needle member and a needle motion controller, hereafter NMC, cooperating with the inner face of said body to divide said inner space in an upstream chamber and a downstream chamber, the NMC being provided with a variable fluid communication comprising the fixed damping fluid communication and the unrestricted fluid communication between said chambers (UC, DC), said variable fluid communication (F1, F2) evolving from a restricted flow state, when the valve assembly is in a closed position preventing fuel injection, to an unrestricted flow state when the valve assembly is lifted away from said closed position, wherein the fixed fluid communication is active when the valve assembly is in closed position and, the unrestricted fluid communication is inactive in closed position and, becoming active and predominant over the fixed fluid communication when the valve assembly lifts away from said closed position, wherein said variable fluid communication comprises a shutter member that activates the unrestricted fluid communication after the needle has lifted away from the closed position and, wherein said shutter member deactivates said unrestricted fluid communication when the valve assembly approaches said closed position, wherein said NMC is a collar member defining an outer cylindrical face joining an upstream face partly defining the upstream chamber and, a downstream face partly defining the downstream chamber, said unrestricted fluid communication comprising inner channels opening in said outer face, wherein the shutter member is integral to the wall of the body, wherein the inner section of the downstream chamber is narrower than the inner section of the upstream chamber, the inner face of the wall being provided with an annular shoulder joining said different sections, the shutter member being defined by the portion of the narrower wall next to said shoulder and, wherein, in a closed position of the valve assembly, the shutter closes the opening of the inner channel arranged in the NMC outer face, the variable fluid communication (F1, F2) being in a closed state and wherein, a needle motion toward the open position moves said channel aperture in the larger upstream portion where it uncovers and opens beyond said shoulder face, opening said unrestricted fluid communication. wherein the fixed fluid communication is active when the valve assembly is in closed position and, the unrestricted fluid communication is inactive in closed position and, becoming active and predominant over the fixed fluid communication when the valve assembly lifts away from said closed position, wherein said variable fluid communication comprises a shutter member that activates the unrestricted fluid communication after the needle has lifted away from the closed position and, wherein said shutter member deactivates said unrestricted fluid communication when the valve assembly approaches said closed position, wherein said NMC is a collar member defining an outer cylindrical face joining an upstream face partly defining the upstream chamber and, a downstream face partly defining the downstream chamber, said unrestricted fluid communication comprising inner channels opening in said outer face, wherein the shutter member is integral to the wall of the body, wherein the inner section of the downstream chamber is narrower than the inner section of the upstream chamber, the inner face of the wall being provided with an annular shoulder joining said different sections, the shutter member being defined by the portion of the narrower wall next to said shoulder and, wherein, in a closed position of the valve assembly, the shutter closes the opening of the inner channel arranged in the NMC outer face, the variable fluid communication (F1, F2) being in a closed state and wherein, a needle motion toward the open position moves said channel aperture in the larger upstream portion where it uncovers and opens beyond said shoulder face, opening said unrestricted fluid communication.