Yes, the ability will trigger (not activate). Since the Parting doesn't say to move it to another zone, they're still a part of your library until you put them into your hand/graveyard. The Blessing will go to the graveyard from your library, so its ability will trigger.
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DCI Level 2 Judge
Scientists have calculated that the chance of anything so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.
The second card you find with Final Parting is put directly into the GY from the library and as a result will trigger the second ability of Gaea's Blessing to shuffle your GY.
Gaea's Blessing second ability says if it is put into a graveyard from the library, shuffle your graveyard into your library.
My question is does discarding Gaea's Blessing with Final Parting activate its second ability?
Scientists have calculated that the chance of anything so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.
Gaea's Blessing
The second card you find with Final Parting is put directly into the GY from the library and as a result will trigger the second ability of Gaea's Blessing to shuffle your GY.