We propose a formation mechanism for twin blue stragglers (BSs) in compact binaries that involves mass transfer from an evolved outer tertiary companion on to the inner binary via a circumbinary disk. We apply this scenario to the observed double BS system Binary 7782 in the old open cluster NGC 188, and show that its observed properties are naturally reproduced within the context of the proposed model. We predict the following properties for twin BSs: (1) For the outer tertiary orbit, the initial orbital period should lie between 220 days $lesssim$ P$_{rm out}$ $lesssim$ 1100 days, assuming initial masses for the inner binary components of $m_{rm 1} = 1.1$ M$_{odot}$ and $m_{rm 2} =$ 0.9 M$_{odot}$ and an outer tertiary mass of $m_{rm 3} = 1.4$ M$_{odot}$. After Roche-lobe overflow, the outer star turns into a white dwarf (WD) of mass 0.43 to 0.54,MSun. There is a correlation between the mass of this WD and the outer orbital period: more massive WDs will be on wider orbits. (3) The rotational axes of both BSs will be aligned with each other and the orbital plane of the outer tertiary WD. (4) The BSs will have roughly equal masses, independent of their initial masses (since the lower mass star accretes the most). The dominant accretor should, therefore, be more enriched by the accreted material. Hence, one of the BSs will appear to be more enriched by either He, C and O or by s-process elements, if the donor started Roche lobe overflow on, respectively, the red giant or asymptotic giant branch. (5) Relative to old clusters, twin BSs in close binaries formed from the proposed mechanism should be more frequent in the Galactic field and open clusters with ages $lesssim$ 4-6 Gyr, since then the donor will have a radiative envelope. (6) The orbit of the binary BS will have a small semi-major axis (typically $aplt 0.3$,au) and be close to circular ($e aplt 0.2$).
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