You are quite correct, the melody in question is "Våren" (The Spring) from "To elegiske melodier for strykeorkester""Två elegiska melodier för stråkorkester""Two Elegiac Melodies for Strings". The other melody of the two is "Hjertesår" (Heart wounds), which I did not find in any free, easily linkable version online.

Source: Complete list of Griegs works at the Grieg Museum Troldhaugen (in norwegian). It is Op34, so scroll down a bit.

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