Can an earthquake occurring within two plates trigger another earthquake in a far away plate boundary?
I guess that it is possible.

As mentioned by others, on top of static stress triggering, which is the effect of an earthquake in its vicinity (typically up to 2-3 rupture lengths away), another way by which an earthquake can trigger others is by dynamic stress triggering, which may have effects farther away but are hard to identify and measure.

So far, the only earthquake that seems to have demonstrated how dynamic triggering over long distances can take place is the 2012 Indian Ocean earthquakes. This earthquake had an unusual combination of characteristics: it was a very large strike-slip earthquake, it took place in oceanic crust (which allows surface waves to travel longer) and had a very large concentrated burst of Mw 8.4 - 8.5 with large slip over limited distance (I do not post sources since there are at least 3 apparently good studies with very different results, for example one study says that slip exceeded 80m locally (!)). These characteristics suggest that this earthquake was very efficient at radiating energy through the crust rather than towards the interior or through very fragmented crust.

So, what this earthquake showed, is that it is possible to speed up significant earthquakes (earthquakes that were almost ready to happen, but they were sped up up to 90 days). Still, it is only one case, the mechanism is not well understood, we are not sure why this earthquake seemed to have caused this phenomenon while other earthquakes with higher magnitudes did not show the same effects.

Concluding, while static stress triggering has only a fairly local effect, dynamic stress triggering may have a wider effect but we only have detected one such case, which could very well have been a coincidence or due to an unusual mechanism. So the answer to your question seems to be yes, but with doubts and in any case for very special earthquakes.