This particular 四字熟語 is exactly the same as the proverb in English, "kill two birds with one stone." I find it to be a strange coincidence that both would have this phrase independently of each other, unless killing birds by throwing stones was just a really big thing back then. Did the Japanese copy the English? Did the English copy the Japanese? Did they both copy some Chinese proverb or something, or did it come from somewhere else entirely? Etymologically speaking where did 一石二鳥 come from?
And I'll go ahead and give an answer to this as well:
According to this, it was translated directly from English into a 四字熟語. This is interesting to me considering that 一挙両得 already exists and means basically the same thing.
According to this site, it was introduced as a phrase in Meiji Japan and then later made into 4 characters. I don't know the origin of the phrase in English, but that's out of the purview of this site!
Just makes me wonder what other proverbs were taken from English and made into 四字熟語.
Although 故事ことわざ辞典 says 一石二鳥 is a direct translation of ”kill two birds with one stone” into the form of 四字熟語 (Chinese / Japanese idioms composed of four characters), I’m not sure of it, because the Chinese have exactly the same phrase
一石二鳥 (yī shí èr niǎo).
We might have imported 一石二鳥 from Chinese, or the Chinese imported the proverb we translated from English proverb, I don’t know.
As an antonym to 一石二鳥, we have
He who chases two hares catches neither.
Again, I can’t tell whether this is the translation of the English proverb or not.