Context : Aims : We have discovered a strong lensing fossil group ( J0454 ) projected near the well-studied cluster MS0451-0305 . Using the large amount of available archival data , we compare J0454 to normal groups and clusters . A highly asymmetric image configuration of the strong lens enables us to study the substructure of the system . Methods : We used multicolour Subaru/Suprime-Cam and CFHT/Megaprime imaging , together with Keck spectroscopy to identify member galaxies . A VLT/FORS2 spectrum was taken to determine the redshifts of the brightest elliptical and the lensed arc . Using HST/ACS images , we determined the group ’ s weak lensing signal and modelled the strong lens system . This is the first time that a fossil group is analysed with lensing methods . The X-ray luminosity and temperature were derived from XMM-Newton data . Results : J0454 is located at z = 0.26 , with a gap of 2.5 mag between the brightest and second brightest galaxies within half the virial radius . Outside a radius of 1.5 Mpc we find two filaments extending over 4 Mpc , and within we identify 31 members spectroscopically and 33 via the red sequence with i < 22 mag . They segregate into spirals ( \sigma _ { v } = 590 ~ { } km~ { } s ^ { -1 } ) and a central concentration of ellipticals ( \sigma _ { v } = 480 ~ { } km~ { } s ^ { -1 } ) , establishing a morphology-density relation . Weak lensing and cluster richness relations yield consistent values of r _ { 200 } = 810 - 850 kpc and M _ { 200 } = ( 0.75 - 0.90 ) \times 10 ^ { 14 } { M _ { \odot } } . The brightest group galaxy ( BGG ) is inconsistent with the dynamic centre of J0454 . It strongly lenses a galaxy at z = 2.1 \pm 0.3 , and we model the lens with a pseudo-isothermal elliptical mass distribution . A high external shear , and a discrepancy between the Einstein radius and the weak lensing velocity dispersion requires that the BGG must be offset from J0454 ’ s dark halo centre by at least 90 - 130 kpc . The X-ray halo is offset by 24 \pm 16 kpc from the BGG , shows no signs of a cooling flow and can be fit by a single \beta -model . With L _ { X } = ( 1.4 \pm 0.2 ) \times 10 ^ { 43 } ~ { } erg~ { } s ^ { -1 } J0454 falls onto standard cluster scaling relations , but appears cooler ( T = 1.1 \pm 0.1 keV ) than expected ( T \sim 2.0 keV ) . Taken all together , these data indicate that J0454 consists of two systems , a sparse cluster and an infalling fossil group , where the latter seeds the brightest cluster galaxy . An alternative to the sparse cluster could be a filament projected along the line of sight mimicking a cluster , with galaxies streaming towards the fossil group . Conclusions :