If the Post correspondence problem were decidable, then the acceptance problem for Turing machines would be decidable as well (Sipser, Theorem 5.15, as a many-one reduction). From a machine $M$ and an input $w$ one constructs, by Sipser's seven kinds of dominos, an instance whose matches are exactly the accepting computation histories of $M$ on $w$ — the strings $\#\,C_1\,\#\,C_2\,\#\cdots\#\,C_k\,\#$ of consecutive configurations from $q_0 w$ to a configuration in the accept state, each obtained from the previous one by a step of the machine; the passage through the modified problem, in which a match must start with the first domino, is the $\star$ trick. The construction is effective, indeed primitive recursive, which is the part of the argument that the textbook takes for granted.