Recently completed a similar task, but chose to leave the old regulator and inoperable shut-off valve intact. Here is the end result – (sorry about the debris and couple of messy solders)
Lots of good info in the previous posts. Hobie I will have to steal the wonder bread trick, and give the squirt bottles some rest. Here are some of the tools that made the soldering work a bit easier.
After working with different solders, these days I swear by this one – https://www.lowes.com/pd/Worthington-16-oz-Lead-Free-Copper-Pipe-Solder/3819167. They melt like butter and provide a pretty leak free joins. A generous amount of water soluble flux (purchased at Fergusons) at the fittings end also helps. Couple of precautionary steps included wrapping the new and old regulators with dripping moist towels to avoid any heat damage, 2) the wall covered with a few layers of aluminum foil sheets to avoid flame burns. In this particular project, there was a bit of struggle connecting to the old section, which resulted in some flame burns on the wall!