1/2 in. Copper Pressure Cup x Cup Coupling Fitting with Stop

The cheapest and best route as stated would be to get a longer braided line. You can cut off the copper pipe or Dremel tool cut off the copper supply line fitting's brass ring, respectively. Be very careful cutting off the old brass compression ring on the old pipe, now exposed. Do not nick the copper pipe. Solder sweat on a 1/2" elbow. Install a short 1/2" copper pipe piece needed to reach the braided line area. Install another copper 1/2" elbow pointing up. Install a short piece of 1/2" copper pipe. Sweat on or compression ring (yuk) install a new Quarter Turn *leak proof* Teflon stem valve, that is a sweat 1/2" pipe to 3/8" compression ring valve. The best wetting sweating solder to use is any old 50:50 Lead-Tin solid solder you might have. It is not sold for plumbing anymore. It is used as stain glass solid solder. The new solders do not wet copper even if you use the best Nokarode brand self cleaning acid flux, IMO. If you don't have old 50-50 solder, go the longer braided line route or try antimony solder. Practice using antimony based solder on loose fittings to make sure you can get it to flow. I can't. The joint lead in pipes builds up overnight when water is standing. You have old solder looking pipes in the picture. The first thing you do in the morning when you get up is flush the lines using a toilet. New lower or no metals city water is run into the lines. Always run the kitchen branch cold water for 30 second before making coffee to flush the overnight standing water in old 50-50 soldered joints and lines not cleared by the toilet flush. HTH

Actual vernier caliper values for these one inch copper pieces are: Couple length: 1.980", 50.29 mm Coupling ID: 1.125", 28.58 mm Coupling OD: 1.232", 31.29 mm L 1" Pipe OD: 1.927", 16.10 mm L 1" Pipe ID: 1.128", 28.50 mm Fitting to copper L type pipe clearance? Three thousandths of an inch, 0.003"

No, it will not work with typical refrigerator soft copper tubing that measures 1/4" outside diameter (OD). Nominal diameter for 1/4" pipe is an internal measurement meaning that the outside of the pipe (and the inside of this 1/4" couple) will be larger than 1/4." I think I've used nominal 1/8" couples to join 1/4" OD pipe, but it was a long time ago so caution to verify fit before you buy.

1 inch copper has an outer diameter of 1.125 and an inner diameter of 1 inch. This coupling is designed to couple two 1" copper pipes over the outside of those pipes. Hopefully you meant diameter and not circumference which is defined as 2*pi*r or d*pi. If you have a standard 1" copper pipe (not tubing) then this should work for you.