3 months x 0.2c = a distance of 0.05 light years between them, or 470 billion kilometers.
For comparison, Voyager 1 is currently just over 20 billion kilometers away. We can just about receive a message from it, since:
1. It has a radioactive power source, currently generating about 250 watts
2. It has directional antenna
3. We capture it using a network of huge antennas around the earth.
"The sensitivity of our deep-space tracking antennas located around the world is truly amazing. The antennas must capture Voyager information from a signal so weak that the power striking the antenna is only 10 exponent -16 watts (1 part in 10 quadrillion). A modern-day electronic digital watch operates at a power level 20 billion times greater than this feeble level."
Now try to make a postage stamp which works as well as this - both as transmitter and receiver. Oh, and make it work over a distance 25 times larger, so the signal is 625 times weaker.