The aim of the Laser Interferometer Space Antenna (LISA) is to detect gravitational waves through a phase modulation in long (2.5 Mkm) laser light links between spacecraft. Among other noise sources to be addressed are the phase fluctuations caused by a possible angular jitter of the emitted beam. The present paper follows our preceding one (Vinet et al 2019 Class. Quant. Grav. 36, 205 003) based on an analytical study of the far field phase. We address here a numerical treatment of the phase, to first order in the emitted wavefront aberrations, but without any assumptions on the static bias term. We verify that, in the phase change, the higher order terms in the static mispointing are consistent with the results found in our preceding paper.