The binary star WOCS 5379 has a blue straggler star (BSS) with a helium white dwarf (WD) companion in a 120-day orbit. The WD and the period suggest that the BSS is the result of previous mass transfer from a red giant donor star. WOCS 5379 is a member of the NGC 188 open cluster, whose age (7 Gyr), metallicity (solar) and other important parameters are well constrained, making it an excellent system with which to test mass transfer stability and binary evolution theory. Detailed models of the system evolution are made using the Modules for Experiments in Stellar Astrophysics (MESA) binary module. WOCS 5379 is well-reproduced with a donor star having an initial mass of 1.19 M⊙, whose core becomes the WD. The model accretor star, which becomes the BSS, initially is a 1.01 M⊙ secondary main-sequence star. The mass transfer (MT) efficiency is 22% (22% of the mass loss from the donor star goes to the accretor), which is the maximum MT efficiency that can maintain stable mass transfer at this mass ratio based on our simulation. The factor that affects the stability of the MT is also discussed. After receiving mass from the donor, the accretor is rejuvenated and becomes a BSS of NGC 188. The authors acknowledge funding support from NSF AST-1714506.