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Does there exist, for every generating $n$-tuple $(h_1,\\ldots, h_n)$ of $H$, a homomorphism $\\vartheta \\colon G \\to H$ and a generating $n$-tuple $(g_1,\\ldots,g_n)$ of $G$ such that $(g_1^\\vartheta,\\ldots,g_n^\\vartheta) = (h_1,\\ldots,h_n)$?\n  M.J. Dunwoody gave a negative answer to this question, by means of a carefully engineered construction of an explicit pair of soluble groups. 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