Place the Ag particles near the emitting shell, along the outer sidewalls or accessible shell at the base. Its emission is close to the localized surface plasmon resonance; the core emission is more detuned and farther from an externally placed particle. The plasmon near field decays with distance, so the local emitter-field overlap matters as well as spectral overlap. A thin spacer can reduce direct-contact nonradiative quenching.
These facts identify a favourable placement for enhanced interaction; they do not by themselves prove the spectroscopic strong-coupling regime, which additionally requires coherent coupling to exceed the relevant losses and normally produces resolvable mode splitting.

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