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We present the study of the south-west group in the Fornax cluster centred on the brightest group galaxy (BGG) Fornax A, observed as part of the Fornax Deep Survey (FDS). This includes the analysis of the bright group members (mB < 16 mag) and the intra-group light (IGL). The main objective of this work is to investigate the assembly history of the Fornax A group and to compare its physical quantities as a function of the environment to that of the Fornax cluster core. For all galaxies, we extract the azimuthally averaged surface brightness profiles in three optical bands (g, r, i) by modelling the galaxy's isophotes. We derive their colour profiles and structural parameters in all respective bands. The long integration time and large covered area of the FDS allow us to also estimate the amount of IGL. The majority of galaxies in the Fornax A group are late-type galaxies (LTGs), spanning a range of stellar mass of $8 < log (M_* M_{\odot}) < 10.5$. Six out of nine LTGs show a Type III (up-bending) break in their light profiles, which is either suggestive of strangulation halting star-formation in their outskirts or their HI-richness causing enhanced star-formation in their outer-discs. The estimated luminosity of the IGL is $6 \pm 2 \times 10^{10} L_{\odot}$ in g-band, which corresponds to about 16% of the total light in the group. The Fornax A group appears to be in an early stage of assembly with respect to the cluster core. The environment of the Fornax A group is not as dense as that of the cluster core, with all galaxies except the BGG showing similar morphology, comparable colours and stellar masses, and Type III disc-breaks, without any clear trend of these properties with group-centric distances. The main contribution to the IGL is from the minor merging in the outskirts of the BGG NGC1316 and, probably, the disrupted dwarf galaxies close to the group centre.