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We studied theoretically the evolution of excitonic properties of GaSb quantum ring located inside the AlAs/GaAs/InGaAs/AlAs double quantum well with the wells (GaAs and InGaAs) thicknesses. The quantum ring is placed between the wells. In this type II nanostructure, the hole is confined inside the quantum ring and the electron is confined in the GaAs and InGaAs layers. The hole and the electron states were computed using the effective mass and the Hartree approximations. Then, the exciton energy, binding energy and lifetime were calculated. We found that varying the thickness of the well, we can control the localization of the electron wavefunction. Indeed, it can be above or below the quantum ring depending on the thicknesses of the GaAs and InGaAs layers. This has an important influence on the overlapping of the electron wavefunction with that of the hole which rests confined inside the quantum ring. Consequently, we can manipulate the excitonic properties, like energy, binding energy and lifetime via the electron and hole wavefunctions overlap. Thus, the studied systems can be used in tunable nano-optoelectronic devices. Furthermore, the use of the InGaAs layer as a capping layer of the quantum ring, instead of the GaAs layer as in an ordinary quantum ring, allows preserving the original properties of this nanostructure before the deposition of the capping layer. [ABSTRACT FROM AUTHOR]