In a recent paper Phys. Rev. D 98, 074023 (2018), the most up-to-date experimental data for all measured production and decay channels of the bottomoniumlike states Zb(10610) and Zb(10650) were analyzed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange and a short-ranged potential nonperturbatively. All parameters of the interaction were fixed directly from data, and pole positions for both Zb states were determined. In this work we employ the same approach to predict in a parameter-free way the pole positions and the line shapes in the elastic and inelastic channels of the (still to be discovered) spin partners of the Zb states. They are conventionally referred to as WbJ's with the quantum numbers JPC = J++ (J = 0, 1, 2). It is demonstrated that the results of our most advanced pionful fit, which gives the best χ2/d.o.f. for the data in the Zb channels, are consistent with all WbJ states being above-threshold resonances which manifest themselves as well-pronounced hump structures in the line shapes. On the contrary, in the pionless approach, all WbJ's are virtual states which can be seen as enhanced threshold cusps in the inelastic line shapes. Since the two above scenarios provide different imprints on the observables, the role of the one-pion exchange in the B(*)B¯(*) systems can be inferred from the once available experimental data directly.