Curie wants to become human, or as close to it as she can better pursue her studies. The Sole Survivor needs to find an expert; a brain surgeon, an AI programmer, or similar.
Gain enough loyalty with Curie until it opens up. The robot will express the desire to be ported into a human body, if possible.
Head to Goodneighbor and talk to Doctor Amari. She will suggest that a robotic mind like Curie's can be downloaded into a third generation synth, thanks to their brain, bridging human and robotic minds. She does, in fact, have a spare synth around: G5-19's mind did not survive the process of wiping her memories for the Railroad, resulting in a perfectly functional shell that simply lacks a working mind.
Amari will request a 24 hour waiting period to contact the synth's caretaker, Glory. Glory will be resistant to the procedure, but can be persuaded to part with her (by stating the obvious, her friend is already dead, or emphasizing her ability to still help another).
Afterwards, it's a simple matter of watching the download procedure and talking to Curie upon completion (and equipping it, or rather, her, with some new gear).
Find someone to help Curie
Curie wants to become human, or as close to it as she can better pursue her studies. We need to find an expert; a brain surgeon, an AI programmer, or similar.
Bring Curie to Doctor Amari
If Curie seriously wants to become human the logical person to help is Doctor Amari. With her expertise with the memory pods and Synths, perhaps Curie could get her wish.
Wait for Doctor Amari
Doctor Amari's memory operations don't always go well. There's a brain dead Synth that may be a good host for Curie. Doctor Amari needs time to contact the Synth's caretaker.
Talk to the caretaker
G5-19's caretaker has arrived. I need to convince her that she should donate G5's body to Curie.
Watch the download procedure
With consent granted, Doctor Amari is ready to download Curie into G5-19. Hopefully the procedure will work successfully.
Talk to Curie
The operation appears successful. I should talk with Curie to make sure it's really her and she's healthy.
Incredibly, Curie has been downloaded into a Synth body. This is obviously going to be a major adjustment for her. She'll need me more than ever.