We exploit the three-dimensional (3D) character of the strain field created around InGaN islands formed within the multilayer structures spaced by a less than 1-nm-thick GaN layer for the creation of spatially correlated electronically coupled quantum dots (QDs). The laterally inhomogeneous vertical out-diffusion of In atoms during growth interruption is the basic mechanism for the formation of InGaN islands within as-deposited 2D layers. An anisotropic 3D strain field created in the first layer is sufficient to justify the vertical correlation of the islands formed in the upper layers spaced by a sufficiently thin GaN layer. When the thickness of a GaN spacer exceeds 1 nm, QDs from different layers under the same growth conditions emit independently and in the same wavelength range. When extremely thin (less than 1 nm), a GaN spacer is formed solely by applying short GI, and a double wavelength emission in the blue and green spectral ranges evidences the electromechanical coupling. With k→·p→ calculations including electromechanical fields, we model the optoelectronic properties of a structure with three InGaN lens-shaped QDs embedded in a GaN matrix, with three different configurations of In content. The profiles of the band structures are strongly dependent on the In content arrangement, and the quantum-confined Stark effect is significantly reduced in a structure with an increasing gradient of In content from the top to the bottom QD. This configuration exhibits carrier tunneling through the QDs, an increase of wave functions overlap, and evidence emerges of three distinct peaks in the spectral range.