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We continue our study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790[hep-th] and arXiv:1406.0179[hep-th]], with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179[hep-th]], which corresponds to a change of variables with functionally-dependent parameters $\lambda_{a}=U_{a}\Lambda$ induced by a finite Bosonic functional $\Lambda(\phi,\pi,\lambda)$ and by the anticommuting generators $U_{a}$ of BRST-antiBRST transformations in the space of fields $\phi$ and auxiliary variables $\pi^{a},\lambda$.
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