= Solution
An asymmetric film with a B-preferring substrate must have an \b[A-preferring atmosphere interface]. A parallel stack with half-integer thickness $2.5L_0$ can terminate correctly at both surfaces. For equal block widths, one explicit sequence from bottom to top is
$$
\boxed{\mathrm{B}_{L_0/4}\mid\mathrm{A}_{L_0/2}\mid\mathrm{B}_{L_0/2}\mid\mathrm{A}_{L_0/2}\mid\mathrm{B}_{L_0/2}\mid\mathrm{A}_{L_0/4}.}
$$
The thicknesses add to $2.5L_0$, with $1.25L_0$ of each block. B contacts the substrate and A contacts the atmosphere, as shown in the accompanying schematic. The alternating widths in the interior reflect half-period domains, while the terminal domains are half of an interior domain in this idealized construction.
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