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Compression fitting will be the quickest and easyest way,brazing I wouldnt recomend,because this line is for ice & drinking water,if you are going to solder make sure it has a low silver & lead content older spools kicking around on the work bench may have a high content also try to drain the water feed line the best you can,with water in the line it will be a constant heatsync so turn off the valve I guess located in the basement and losen the compression fitting by the valve put the line in a cup or suspend it over a bucket then go to the fridge and depress the water leaver this should break the vaccum and drain out any water that will escape.

I would go the easy way out get the $3.00 compression fitting cut the line ream out the newly cut line and add the diff.