icemaker spigot to shut off valve attachment

I have a cold water lead [1/4 copper pipe] which brings water to the refrig erator icemaker. On the icemaker, I have a 3/4" to 3/8" elbow. I am tryin g to find a fine threaded coupler which would join this to the shut off val ve which has a 3/8 male end on each side. Is there such a thing? I found a coupler at Home Depot, but it is a course thread. Previously, there was a 1/4 copper pipe between the two, which broke when I was moving the refrigerator, so I'd like to use a coupler joint between th e two. Should I buy the course treaded one and have it retreated? Who would do th is? I went to a plumbing store, who told me to go to an appliance store. Home Depot people tried to sell me things that were the right parts as all.
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On Wed, 11 Jul 2018 10:12:59 -0700 (PDT), Deodiaus

The only fine threads in plumbing are for flare nuts or compression nuts so I suspect you are looking at a compression fitting without a nut. They do make hoses with 3/8" compression nut threads. (actually closer to 1/2" diameter). The one you call 3/4" might actually be 1/2" pipe thread if it is "course". They have that hose too (1/2" NPT to 3/8" compression). It will be near the faucet stuff.
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