You will need a flaring tool. rent or buy cheap.
1. Disconnect the hot water line from the existing tee.
2. Cut the hot water line shorter using a pipe cutter. Cut it more than 5 inches away from the existing tee.
3. Put the nut on the copper line that you just cut.
4. Flair the line on the water heater side.
5. Connect a 3-way male tee to the hot water side.
6. With the copper pipe you just cut eyeball measure how much to cut off so you can splice it in between the new tee and the existing tee.
7, Put two 3/8th nuts on the little copper pipe with threads facing out (note, you should have cut this small piece big enough to get two nuts on and still have room to flair it with the tool).
8. Flair the little copper pipe.
9. Attach the little copper pipe to both the new and the old tee.
10 The 3rd tee male fitting is available for your new appliance, so put a nut on a new pipe and flair it and attach.
so, looks like this requires 3 new 3/8 nuts.
If you have never flared then research carefully or else you WILL have a leak. It involves cleaning the fresh cut copper pipe to get rid of burrs and to return the pipe to a constant diameter and also flaring the pipe enough to make a good seal. Best if you find detailed instructions with video or photos.
