Fossil groups are considered the end product of natural galaxy group evolution in which group members sink towards the centre of the gravitational potential due to dynamical friction, merging into a single, massive, and X-ray bright elliptical. Since gravitational lensing depends on the mass of a foreground object, its mass concentration, and distance to the observer, we can expect lensing effects of such fossil groups to be particularly strong. This paper explores the exceptional system J143454.4+522850 (with a lens redshift zL = 0.625). We combine gravitational lensing with stellar population synthesis to separate the total mass of the lens into stars and dark matter. The enclosed mass profiles are contrasted with state-of-the-art galaxy formation simulations, to conclude that SW05 is likely a fossil group with a high stellar to dark matter mass fraction (0.027 ± 0.003) with respect to expectations from abundance matching (0.012 ± 0.004), indicative of a more efficient conversion of gas into stars in fossil groups.