Motovilov A.K. REPRESENTATIONS FOR THREE-BODY T-MATRIX ON UNPHYSICAL SHEETS (Part II): PROOFS. Preprint JINR E5-95-46. To appear in Teoreticheskaya i Matematicheskaya Fizika, 1996 (English translation in Theor. Math. Phys.) 20 pages (94K, LaTeX) ABSTRACT. A proof is given for the explicit representations which have been formulated in the author's previous work for the Faddeev components of three-body $T$-matrix continued analytically on unphysical sheets of the energy Riemann surface. Also, the analogous representations for analytical continuation of the three-body scattering matrices and resolvent are proved. An algorithm to search for the three-body resonances on the base of the Faddeev differential equations is discussed.