In part I [Abh. Math. Semin. Univ. Hamb. 75, 97--120 (2005; Zbl 1088.11032)], the author studied whether a congruence for Fourier coefficients of Siegel modular forms is preserved under Eisenstein lifts. Now he proves criteria for the preservation of such congruences under two types of lifts [\textit{T. Ikeda}, Ann. Math. (2) 154, No. 3, 641--681 (2001; Zbl 0998.11023) and Duke Math. J. 131, No. 3, 469--497 (2006; Zbl 1112.11022)], where he uses the linear expression for the lifts as given by \textit{W. Kohnen} [Math. Ann. 322, No. 4, 787--809 (2002; Zbl 1004.11020)]. Reproducing the criteria would be lengthy. Therefore only an example is quoted here: For \(k\in\{6,10\}\), let \(\Delta_{2k}\in S^2_{2k}\) and \(G_{2k}\in M^1_{2k}\) be the normalized cusp forms and Eisenstein series of weight \(2k\) for \(\Gamma_1= \text{SL}_2(\mathbb{Z})\). They satisfy the Ramanujan congruences \(\Delta_{12}\equiv G_{12}\pmod{691}\) and \(\Delta_{20}\equiv G_{20}\pmod{283\cdot 617}\). Let \(\rho_k\) be the inverse of the Shimura correspondence, mapping \(M^1_{2k}\) to the Kohnen plus space \(M^+_{k+1/2}(\Gamma_0(4))\), and for \(k\geq 2\), \(n\equiv k\pmod 2\), let \(\tau^{2n}_{n+k}\) be the Ikeda lift, mapping \(M^+_{k+1/2}(\Gamma_0(4))\) to the space \(M^{2n}_{n+k}\) of Siegel modular forms of genus \(2n\) and weight \(n+ k\). Then the Ramanujan congruences yield the congruences \(\delta_{13/2}\equiv {\zeta(-11)\over \zeta(-5)} H_{13/2}\pmod{691}\) and \(\delta_{21/2}\equiv{\zeta(-19)\over \zeta(-9)} H_{21/2}\pmod{283\cdot 617}\) with normalized cusp forms \(\delta_{k+1/2}\) in the Kohnen plus spaces and the Cohen-Eisenstein series \(H_{k+1/2}\in M^+_{k+ 1/2}(\Gamma_0(4))\) of the indicated weights, and one obtains congruences \(\tau^{2n}_{n+ 6}(\delta_{13/2})\equiv a_n E^{(2n)}_{n+ 6}\pmod{691}\) for even \(n\geq 6\), \(2\leq n\leq 94\), with the Siegel-Eisenstein series \(E^{(2n)}_{n+ 6}\) of genus \(2n\) and weight \(n+ 6\), and with explicitly given constants \(a_n\).