= Solution
Use one label for each member of $A$. More explicitly, set
$$
T_A=\{((a,\ldots,a),a\mathbin{\upharpoonright}n):a\in A,\ n<\omega\}
\subseteq(A\times\omega)^{<\omega}.
$$
An infinite branch through this <tree> has a constant first coordinate $a\in A$ and second coordinate $a$, so $p[T_A]=A$. Thus $A$ is $A$-Suslin. Since $A\subseteq\omega^\omega$ injects into a set of <cardinal number>[cardinality] $2^{\aleph_0}$, part i makes $A$ a $2^{\aleph_0}$-<Kappa-Suslin set>[Suslin set]. This proves that <Every set of reals is continuum-Suslin>.
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