How do I secure a copper pipe going through a wall?
Use a stainless steel hose clamp (sometimes called a worm clamp becasue of the screw it uses) and a couple of L-brackets  - clamp the L-brackets to the pipe using the hose clamp, screw them into the wall with wood screws.




The fussiest, hardest to find and most expensive aproach would be to find copper or copper-plated L-brackets ("pipe strap" would be easier to find but less rigid.) 

The practical, less expensive and just as functional approach is to use steel L-brackets and place some durable plastic or rubber material between them and the copper pipe to prevent corrosion. Clamping steel directly to copper will result in galvanic corrosion and an eventual leak. 

You can also use stand-off clamps intended for wall mounting on the vertical portion of the pipe.  

The "long-gone plumber" certainly does not appear to have worked to normal plumbing standards...