In our recent NRSE experiment on the quasi two-dimensional quantum spin liquid PHCC at TRISP at FRM-II, we have found a zero field splitting (ZFS) of the magnon line of about 50 mueV at the antiferromagnetic zone centre (0.5,0,-0.5) at T = 0.5 K. Moreover, it is known that the single-magnon dispersion in PHCC submerges into the multi-magnon continuum, thus it becomes unstable for h < 0.15 on the (h,0,-1-h) reciprocal lattice line. Here we propose to study the h dependence of the ZFS width of the magnons in order to compare it with theoretical predictions of its momentum dependence originally established for Haldane chains, also considering its behaviour at the vanishing point of the single-magnon dispersion line at h = 0.15.