= Solution
The finite angular resolution of <COBE DMR> suppresses small angular scales, so only low <spherical harmonic> multipoles can be recovered usefully. The approximate relation $\theta\sim\pi/l$ associates $l\simeq17$ with scales of order ten degrees; this is an effective sensitivity and beam-window limit, not a mathematical hard truncation.
Interpret the printed superscript uncertainty as $(1.1\pm0.1)\times10^{-5}$. Its square estimates the band-limited zero-separation <variance>, rather than the full $C(0)$:
$$
\sigma_{2:17}^2=\frac{1}{4\pi}\sum_{l=2}^{17}(2l+1)C_l
=\frac{0.732\times4.43}{4\pi}\Delta_\phi^2.
$$
Use the coefficient supplied in the paper for this numerical inference. With $\sigma_{2:17}=1.1\times10^{-5}$,
$$
\Delta_\phi^2=4.69\times10^{-10},\qquad H_0=2.269\times10^{-18}\ \mathrm{s^{-1}},
$$
so <3/c> gives
$$
\boxed{A=\frac{8\pi^2c^4\Delta_\phi^2}{9H_0^4}=1.25\times10^{96}\ \mathrm{m^4}=1.38\times10^6\ \mathrm{Mpc^4}.}
$$
The stated amplitude uncertainty gives approximately $18\%$ relative uncertainty in $A$, or $A\simeq(1.38\pm0.25)\times10^6\ \mathrm{Mpc^4}$, keeping $H_0$ fixed. The ideal matter-era <Sachs-Wolfe plateau> with precisely the <3/c> spectrum convention has coefficient $2\pi/9=0.698$, rather than $0.732$; the supplied numerical coefficient is about $5\%$ larger and has been treated as the paper's prescribed approximation. A real beam-convolved analysis retains its window function and additional cosmological transfer effects.
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