= Solution
Construct the times inductively. Suppose $(B_{T_0},\ldots,B_{T_n})$ has the law of $(S_0,\ldots,S_n)$. Conditional on the past, the martingale increment $S_{n+1}-S_n$ has mean zero and finite second moment. Apply the conditional form of the <Skorokhod embedding theorem> to this regular conditional law, using the fresh Brownian motion $B_{T_n+t}-B_{T_n}$ supplied by the <Strong Markov property>. This gives a stopping time increment $\tau_{n+1}$ and $T_{n+1}=T_n+\tau_{n+1}$ such that the next Brownian increment has the required conditional law. Induction proves
$$
(S_0,\ldots,S_k)\stackrel d=(B_{T_0},\ldots,B_{T_k})
$$
for every $k$.
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