The only way to repair a frost proof faucet or, sillcock that has been split from freezing is to replace it with a new one. The tube that has split is an integral part of the valve and is not replaceable. The frost proof sillcocks are designed with an end that can be threaded on or, sweated on. If you were lucky the plumber was a nice guy and installed a female adapter that the sillcock threaded into so replacement is as simple as shutting off the water to the sillcock, taking out the two screws on the outside then with one wrench on the threaded adapter and the other end on the sillcock tube unthreading the bad one then finding a new one the same length applying Teflon tape and Teflon paste to the threads and threading in the new one. However, it is seldom the case that the installing plumber uses a threaded adapter.
Most of the time when you replace a frost proof sill cock you will find the installing plumber sweated it to the copper pipe supplying it. After shutting off the water you will need to cut the pipe then take out the two screws securing the sillcock to the wall outside. You will need a new frost proof sillcock, threaded adapter, extra copper tube, and a repair coupling. You will also have to be able to sweat copper pipe. I usually sweat the threaded adapter onto the copper pipe then cut the pipe and adapter to a length a little longer than what I need. I then apply Teflon tape and Teflon paste to the threads and tighten the threaded adapter and copper pipe stub onto the new frost proof sillcock. I then install it through the outside wall and secure it with the two mounting screws and angle shim. I then go inside and trim the pipes so they meet then I clean and flux the copper tube and repair coupling. The repair coupling does not have a stop in the center so it can be slipped all the way over one of the pieces of copper tube, then I line the two tubes up and slide the repair coupling ½ way on to the other tube so the cut is in the center of the repair coupling. I then sweat the joint turn on the water to the sillcock and check for leaks and proper operation. I then caution the customer that the best way not to do this again is to disconnect the hose over the winter.