Answer: July, 1985.
Explanation: it's a simple problem of speed = distance/time; time = distance/speed.
Since all the rays & signals in the question travel with the speed of light, the time would just be:
Time = (520 light years)/(speed of light) = 520 years.
The explosion happened in 1945, since the sight of the explosion travels at the speed of light, the alien would see the explosion would see the explosion in the year (1945 + 520) = 2465.
The signal sent back to earth would travel at the speed of light too, and it will reach earth in the year (2465 + 520) = 2985.
Meaning the signal will get to earth in July, 2985.
Solved!