An Azcarraga-Lukierski supersymmetric particle model, which is invariant with respect to theN=2 extended SuperPoincare group, is quantised by the method of Dirac brackets. The central charges, which satisfy the spin reducing conditions, are conjugate to additional bosonic coordinates in the superspace. The resulting superwavefunction doublet is in one-to-one correspondence with the superfield expansion of Sohnius describing the Fayet hypermultiplet.