Hmm
You will probably need three straight couplers and a tee at least.
Do you intend to solder it back or use compression fittings?
If you can't see it, probably compression are the best, but they look a bit rough if you can see them. I would advise replacing with the same kind of pipe as that already in, except of course if its lead. If its copper pipe and its an old house, don't forget to bridge the gap where you cut the pipe out of with earthing wire to give earth continuity. There is a good chance unless you know otherwise that the house electrical system could be earthed to the cold main. I've had a belt off one in the past and would not like you or anybody else to get one.
In some shops you can buy repair slip couplers, but they tend to be dear. I would spec on about £1 each for a compression coupler and a bit more for a repair coupler. About £1-50p for a tee and about £1-50p for a metre of 15mm pipe.
Cut back and measure up, then remove the back nuts and rings/olives out of the couplers and slide them onto the pipes, make sure the rings/olives are the right way around. On some makes of compression fitting the rings/olives are meant to go only one way around. The chamfered end toward the fitting usually. Some couplers such as Prestex have a fine thread which is very easy to cross thread so don't force anything, they should run nice and easy if not, look to find out why they don't, don't be tempted to force them on. You may have to file the end of the pipe to get eh rings/olives to go on. Make sure you clear all the filings away and don't wash them down the pipe.
You can then fit it all together like an octopus and angling the couplers and pipe and pushing gently get them back into position. Make sure that you measure the pipe to go full socket into the fittings.
Once together slide the rings and backnuts back onto the fittings applying a bit of potable water, pipe jointing compound, if you have any, make sure it doesn't go inside the pipe. Some makers say you don't need joining compound, but I am old school and try to use it. You can of course use PTFE but it looks a bit mad.
All you are doing is making a face to face metal joint with a bit of softer material as a seal in between. The shape of the ring/olive is so, that as you tighten it, it digs into the pipe and forms a seal.
Then making sure you don't force anything and don't cross thread the back nuts, gently tighten the backnuts up with your hand making sure they run easily up the fitting. Then tighten with a spanner, don't over tighten or under tighten, just so you can feel its got a good grip and won't come loose. Then turn on water slowly checking for leaks as you do so.
With repair couplers, which look like long ordinary couplers, you can slide them up the pipe out of the way and just cut your pipe and tee to fit in the exact space. Then slide them back down the pipe and tighten up. But as I said, they are usually pretty dear.
Just take your time and allow for air locks and the like. Allow time for gathering materials as part of the job time. Then allow time for cutting pipe out. Then for putting back together. Then for testing. Then for airlocks if any. Then for cleaning up.
Then sit down and let your sister fuss about what a clever brother she has got. She might even make you a cup of tea.
Its fairly easy to do by the way, just a bit fiddly.
